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| <!doctype html public "-//w3c//dtd html 4.0 transitional//en"> | |
| <html> | |
| <head> | |
| <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> | |
| <meta name="Author" content="Ellipsa"> | |
| <title>Primo Help Contents</title> | |
| </head> | |
| <body text="#000000" bgcolor="#FFFFFF"> | |
| <font face="Bitstream Vera Serif"> | |
| <center> | |
| <b><font size="+3">PRIMO - Primality Proving</font></b><br> | |
| </center> | |
| <a NAME="Contents"></a> | |
| <hr> | |
| <center> | |
| <br> | |
| <br> | |
| <font size="+2"><b>Contents</b><br></font> | |
| </center> | |
| <br> | |
| <center> | |
| <table border cellspacing="0" cellpadding="8" cols="2" width="80%" bgcolor="#F7F7F7"> | |
| <tr valign="top"> | |
| <td> | |
| <ul> | |
| <font size="+1"> | |
| <li><b>Manual</b></li> | |
| </font> | |
| <ul> | |
| <font size="+1"> | |
| <li><a href="#Overview">Overview</a></li> | |
| <li><a href="#GettingStarted">Getting started</a></li> | |
| <li><a href="#ButtonBar">Button bar</a></li> | |
| <li><a href="#TaskReportPage">Task Report page</a></li> | |
| <li><a href="#CertificationPage">Certification page</a></li> | |
| <li><a href="#VerificationPage">Verification page</a></li> | |
| <li><a href="#Certificate">What is a primality certificate?</a></li> | |
| <li><a href="#Resuming">How to resume a certification?</a></li> | |
| <li><a href="#InternalError">Internal Errors</a></li> | |
| </font> | |
| </ul> | |
| </ul> | |
| </td> | |
| <td> | |
| <ul> | |
| <font size="+1"> | |
| <li><b>Files</b></li> | |
| </font> | |
| <ul> | |
| <font size="+1"> | |
| <li><a href="#InputFile">Input (Candidate)</a></li> | |
| <li><a href="#OutputFile">OutPut (Certificate)</a></li> | |
| <li><a href="#TaskReportFile">Task Report</a></li> | |
| <li><a href="#ReportFile">Certification Report</a></li> | |
| </font> | |
| </ul> | |
| </ul> | |
| <ul> | |
| <font size=+1> | |
| <li><b>Miscellaneous</b></li> | |
| </font> | |
| <ul> | |
| <font size="+1"> | |
| <li><a href="#License">End-User License</a></li> | |
| </font> | |
| </ul> | |
| </ul> | |
| </td> | |
| </tr> | |
| </table> | |
| </center> | |
| <br> | |
| <br> | |
| <center> | |
| <table cellspacing="0" cellpadding="0" cols="1" width="80%"> | |
| </table> | |
| </center> | |
| <br> | |
| <br> | |
| <a NAME="Overview"></a> | |
| <hr> | |
| <center><b><font size="+2">Overview</font></b><br></center> | |
| <hr> | |
| <br> | |
| <blockquote> | |
| <font size="+1"><b>What is PRIMO ?</b><br></font> | |
| <hr> | |
| PRIMO is a primality proving program based on the ECPP algorithm: Elliptic Curve Primality | |
| Proving. Given positive odd integers, PRIMO tests whether these integers are prime, and if | |
| they are it produces <a href="#Certificate">primality certificates</a>.<br> | |
| PRIMO is suitable for the checking of crypto-primes and to prove whether they are actually | |
| prime... or not.<br> | |
| <hr><br> | |
| <b><font size="+1">Latest Release</font></b><br> | |
| <hr> | |
| To check whether you have the most recent version of PRIMO, please, visit the | |
| <a href="http://www.ellipsa.eu/index.html">PRIMO Home page</a><br> | |
| <hr><br> | |
| <b><font size="+1">Contact</font></b><br> | |
| <hr> | |
| Send any comment, suggestion, bug report, whatever to | |
| <a href="mailto:primo@ellipsa.eu">primo@ellipsa.eu</a><br> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="GettingStarted"></a> | |
| <hr> | |
| <center><b><font size="+2">Getting Started</font></b></center> | |
| <hr> | |
| <br> | |
| <blockquote> | |
| <b><font size="+1">File Associations</font></b><br> | |
| <hr> | |
| When running, PRIMO works with the following text files:<br> | |
| <font face="Bitstream Vera Sans Mono"> | |
| <font color="#000099"><b>Primo-xxxxxxxxxxxxxxx.cr</b></font>........</font> | |
| <a href="#ReportFile">Certification Report file</a><br> | |
| <font face="Bitstream Vera Sans Mono"> | |
| <font color="#000099"><b>*.in</b></font>............................</font> | |
| <a href="#InputFile">Input file</a> (Integer to test)<br> | |
| <font face="Bitstream Vera Sans Mono"> | |
| <font color="#000099"><b>Primo-xxxxxxxxxxxxxxx-nnn.out</b></font>...</font> | |
| <a href="#OutputFile">Output file</a> (Primality certificate)<br> | |
| <font face="Bitstream Vera Sans Mono"> | |
| <font color="#000099"><b>Primo-xxxxxxxxxxxxxxx.tr</b></font>........</font> | |
| <a href="#TaskReportFile">Task Report file</a><br> | |
| <font face="Bitstream Vera Sans Mono" color="#000099"><b>xx..xx</b></font> | |
| is a unique identifier that allows to identify all the files created during | |
| batch processing.</font><br> | |
| <font face="Bitstream Vera Sans Mono" color="#000099"><b>nnn</b></font> | |
| indicates the index (when batch processing) of the tested integer.<br> | |
| In order to open these files with your favorite text editor, you should create | |
| an association <i>File extension - Editor</i> for the extensions <b>.cr</b>, | |
| <b>.in</b>, <b>.out</b> and <b>.tr</b>. If you do not create associations, PRIMO | |
| will use NotePad by default.<br> | |
| <hr><br> | |
| <b><font size="+1">First Session</font></b><br> | |
| <hr> | |
| Run PRIMO.<br> | |
| Click on the <i>Certification</i> button.<br> | |
| In the <a href="#CertificationPage">Certification page</a>, click on the <i>Load file(s)...</i> | |
| button. Select the <i>work</i> directory and double-click on <i>first.in</i>.<br> | |
| When the certification is done, a short report is displayed in the editor of the | |
| <a href="#TaskReportPage">Task Report page</a>. To open a results text | |
| file, double-click on the relevant item.<br> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="ButtonBar"></a> | |
| <hr> | |
| <center><b><font size="+2">Button Bar</font></b></center> | |
| <hr> | |
| <br> | |
| <blockquote> | |
| <b><font size="+1">Buttons</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7" > | |
| <tr> | |
| <td WIDTH="20%"> | |
| <b><font color="#000099">Help</font></b> | |
| </td> | |
| <td> | |
| Open the documentation. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td WIDTH="20%"> | |
| <b><font color="#000099">About Primo</font></b> | |
| </td> | |
| <td> | |
| Open the About dialog box.</td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">New input file</font></b> | |
| </td> | |
| <td> | |
| Create a new empty <a href="#InputFile">input file</a>. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Open a Primo text file</font></b> | |
| </td> | |
| <td> | |
| Open a file list box with which you can select PRIMO text files: input, | |
| <a href="#OutputFile">output</a>, <a href="#TaskReportFile">task report</a> and | |
| <a href="#ReportFile">certification report</a>. These files are open with the text editor | |
| you associated with their extensions (or with NotePad if there is no association). | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Quit</font></b> | |
| </td> | |
| <td> | |
| Close PRIMO. | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <b><font size="+1">Check box</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7" > | |
| <tr> | |
| <td WIDTH="20%" VALIGN=TOP> | |
| <b><font color="#000099">Idle</font></b> | |
| </td> | |
| <td> | |
| When checked, the PRIMO process priority is set to "idle", otherwise it is set to "normal". The | |
| value can be changed while running a task (certification or verification).<br> | |
| <i>Default value = Unchecked</i> (Normal priority) | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="TaskReportPage"></a> | |
| <hr> | |
| <center><b><font size="+2">Task Report Page</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| The Task Report page contains an editor used to display certification and verification reports.<br> | |
| <br> | |
| <b><font size="+1">Report Editor</font></b><br> | |
| <hr> | |
| When an entry in the report contains the name of a PRIMO text file, you can open the | |
| file by double-clicking on the item (alternately, you can select the item with the | |
| Arrow keys and hit the Return key to open the file).<br> | |
| The editor content is automatically saved to a <a href="#TaskReportFile">task | |
| report file</a> (text file).<br> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="CertificationPage"></a> | |
| <hr> | |
| <center><b><font size="+2">Certification Page</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| The Certification page is a dialog box that allows to perform the certification of | |
| integers in PRIMO <a href="#InputFile">input files</a> (and also to resume | |
| aborted certificates). Loading <b>.in</b> files starts certifications. Loading | |
| <b>.tmp</b> files restarts aborted certifications.<br> | |
| The certificates are automatically saved to <a href="#OutputFile">output files</a>, | |
| in the directory that contains the input files.<br> | |
| While certifying, PRIMO creates and updates temporary files having the <b>.tmp</b> extension. | |
| <b>Do not modify them.</b> If you want to edit them (they are text files), make copies | |
| and edit those copies. If ever a <b>.tmp</b> file is modified (some editors add invisible | |
| codes), all the work done may be lost!<br> | |
| See also: <a href="#Certificate">What is a certificate?</a><br> | |
| <br> | |
| <b><font size="+1">Setup</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="27%"><b> | |
| <font color="#000099">Certification reports</font></b> | |
| </td> | |
| <td> | |
| When checked, PRIMO creates <a href="#ReportFile">certification report</a> files.<br> | |
| <i>Default value = Checked</i> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP><b> | |
| <font color="#000099">Double file management</font></b> | |
| </td> | |
| <td> | |
| When checked, even in case of problem when PRIMO is writing on a disk (OS crash, outage, etc.), | |
| there should always be at least one valid file on the disk among these three possible | |
| ones : <b>.tmpnew</b>, <b>.tmp</b> or <b>.tmpold</b>.<br> | |
| Of course, in order to restart PRIMO with one of these files, its extension has to | |
| be set with <b>.tmp</b> (if need be).<br> | |
| This option is useful with very big candidates only.<br> | |
| <i>Default value = Unchecked</i> | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <b><font size="+1">Status</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td WIDTH="25%"> | |
| <b><font color="#000099">Elapsed time</font></b> | |
| </td> | |
| <td>Running time of the certification. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Number</font></b> | |
| </td> | |
| <td> | |
| Number (in the input file list) of the integer that is currently being tested. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Phase</font></b> | |
| </td> | |
| <td> | |
| Number of the current phase (1 or 2).<br> | |
| The <i>Phase 1</i> consists in finding a sequence of pseudoprimes.<br> | |
| The <i>Phase 2</i> consists in building and factoring class polynomials and in computing | |
| elliptic curves and points (which ones prove that the sequence of pseudoprimes found | |
| during <i>Phase 1</i> is in fact a sequence of primes). | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Test</font></b> | |
| </td> | |
| <td>Number of the current test.<br> | |
| The value may decrease due to backtracking. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Run</font></b> | |
| </td> | |
| <td> | |
| Number of the current run (max = 6)<br> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Bits</font></b> | |
| </td> | |
| <td> | |
| Indicates the binary size of the integer currently tested. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Status</font></b> | |
| </td> | |
| <td> | |
| Miscellaneous information regarding the current status of a certification. | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <b><font size="+1">Buttons</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="25%"> | |
| <b><font color="#000099">Load</font></b> | |
| </td> | |
| <td> | |
| Load files and start certifications (and/or restart aborted certifications). The | |
| selected files are always processed in alphabetical order. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Abort</font></b> | |
| </td> | |
| <td> | |
| Allow to abort a certification.<br> | |
| When a certification is aborted, a partial certificate is saved to a file having | |
| the <b>.tmp</b> extension. To restart the certification, just load this file. | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="VerificationPage"></a> | |
| <hr> | |
| <center><b><font size="+2">Verification Page</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| The Verification page is a dialog box that allows to verify and to sign certificates. | |
| Checking can be aborted and resumed (PRIMO restarts from the last test not yet | |
| processed).<br> | |
| The certificates are always verified and signed while certifying.<br> | |
| See also: <a href="#Certificate">What is a certificate?</a><br> | |
| <br> | |
| <b><font size="+1">Setup</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="27%"> | |
| <b><font color="#000099">Check signatures only</font></b> | |
| </td> | |
| <td> | |
| When not checked, PRIMO always verifies the certificate and signs it. If the certificate | |
| is already signed, <b>the existing signature is deleted</b> before starting the verification.<br> | |
| When checked, PRIMO tries to check the signature only (this allows to quickly reject invalid | |
| certificates). If there is no signature section then | |
| it verifies the certificate and signs it.<br> | |
| <i>Default value = Checked</i> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Double file management</font></b> | |
| </td> | |
| <td> | |
| When checked, even in case of problem when PRIMO is writing on a disk (OS crash, outage, etc.), | |
| there should always be at least one valid file on the disk among these three possible | |
| ones : <b>.outnew</b>, <b>.out</b> or <b>.outold</b>.<br> | |
| Of course, in order to restart PRIMO with one of these files, its extension has to | |
| be set with <b>.out</b> (if need be).<br> | |
| This option is useful with very big candidates only.<br> | |
| <i>Default value = Unchecked</i> | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <b><font size="+1">Status</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td WIDTH="27%"> | |
| <b><font color="#000099">Elapsed time</font></b> | |
| </td> | |
| <td> | |
| Running time of the verification. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Certificate</font></b> | |
| </td> | |
| <td> | |
| Number (in the <a href="#OutputFile">output file</a> list) of the certificate | |
| that is currently being verified. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Test</font></b> | |
| </td> | |
| <td> | |
| Number of the current test. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Bits</font></b> | |
| </td> | |
| <td> | |
| Indicates the binary size of the integer currently checked. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font color="#000099">Status</font></b> | |
| </td> | |
| <td> | |
| Miscellaneous information regarding the current status of a verification. | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <b><font size="+1">Buttons</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 COLS=2 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="25%"> | |
| <b><font color="#000099">Load</font></b> | |
| </td> | |
| <td> | |
| Load files and start verifications. The selected files are always processed in | |
| alphabetical order. | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font color="#000099">Abort</font></b> | |
| </td> | |
| <td> | |
| Allow to abort a verification. | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="Certificate"></a> | |
| <hr> | |
| <center><b><font size="+2">Certificate</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| A primality certificate produced by PRIMO is a sequence of tests. Each test, except the | |
| final one, proves that an integer, called N, is prime assuming a smaller integer, called R, | |
| is also prime. Since the R value of a test is used as the N value of the following test, the | |
| primality of the last R value of a certificate proves the primality of the candidate.<br> | |
| PRIMO makes use of up to four different tests.<br> | |
| <b>Note:</b> In what follows, N is always a positive odd integer greater than 65536.<br> | |
| <br> | |
| <b><font size="+1">Strong Pseudoprime Test</font></b><br> | |
| <hr> | |
| In a certificate, this test is identified with <b>Type = 0</b> | |
| <p> | |
| <i>Assuming N < 34 * 10^13,</i><br> | |
| <i>if N is a strong pseudoprime to the bases 2, 3, 5, 7, 11, 13 and 17 then N is prime.</i> | |
| <p> | |
| The first number which is a strong pseudoprime to these seven bases, but not a prime, is | |
| larger than 34 * 10^13.<br> | |
| <hr><br> | |
| <b><font size="+1">N-1 Test</font></b><br> | |
| <hr> | |
| In a certificate, this test is identified with <b>Type = 1</b> | |
| <p> | |
| <i> | |
| Assuming N = S * R + 1 with R prime and S < R,<br> | |
| if there exists an integer B > 1 such that<br> | |
| B^(N-1) = 1 mod N<br> | |
| gcd(B^S - 1, N) = 1<br> | |
| then N is prime.<br> | |
| </i> | |
| <hr><br> | |
| <b><font size="+1">N+1 Test</font></b><br> | |
| <hr> | |
| In a certificate, this test is identified with <b>Type = 2</b> | |
| <p> | |
| <i> | |
| Assuming N = S * R - 1 with R prime and S < R,<br> | |
| if there exists a Lucas sequence V[i], with parameters P and Q, such that<br> | |
| gcd(P, Q) = 1<br> | |
| Jacobi(P² - 4Q, N) = -1<br> | |
| V[(N+1)/2] = 0 mod N<br> | |
| V[S/2] <> 0 mod N<br> | |
| then N is prime. | |
| </i> | |
| <p> | |
| The parameter P is not displayed in PRIMO certificates. When Q is even, P = 1 ; when | |
| Q is odd, P = 2.<br> | |
| <hr><br> | |
| <b><font size="+1">Elliptic Curve Test</font></b><br> | |
| <hr> | |
| In a certificate, this test is identified with <b>Type = 3</b> or with <b>Type = 4</b> | |
| <p> | |
| <i> | |
| Assuming M = S * R, with S > 1, R prime, R > (N^(1/4) + 1)^2,<br> | |
| if there exist a non-singular elliptic curve y^2 = x^3 + ax + b modulo N, with order | |
| M, and a point P = (x, y) on this curve such that<br> | |
| P * S <> Identity<br> | |
| (P * S) * R = Identity<br> | |
| then N is prime. | |
| </i> | |
| <p> | |
| <u>Type = 3</u><br> | |
| The 3 parameters A, B and T, reported in PRIMO certificates, allow to quickly compute | |
| the required curve and point:<br> | |
| L := (T^3 + A*T + B) mod N<br> | |
| a := (A * L^2) mod N<br> | |
| b := (B * L^3) mod N<br> | |
| x := (T * L) mod N<br> | |
| y := (L^2) mod N | |
| <p> | |
| <u>Type = 4</u><br> | |
| The parameter J allows to compute A and B as defined with Type = 3:<br> | |
| A := 3 * J * (1728 - J)<br> | |
| B := 2 * J * (1728 - J)^2<br> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="Resuming"></a> | |
| <hr> | |
| <center><b><font size="+2">Resuming</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| In the <a href="#CertificationPage">Certification page</a>, click on the <i>Load file(s) | |
| and start certification(s)</i> button. Select the <b>.tmp</b> file created when | |
| aborting the certification.<br> | |
| Thats all.<br> | |
| <br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="InternalError"></a> | |
| <hr> | |
| <center><b><font size="+2">Internal Error</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| An internal error may be raised by PRIMO for mainly two reasons: a hardware failure or | |
| a PRIMO bug.<br> | |
| In case such an error occurs, try first to redo what you were doing. If the error still | |
| occurs, thanks to report the problem with the most possible details: OS used, processor | |
| type, partial certificate obtained, etc. as well as a description of the problem, mail | |
| to primo (at) ellipsa (dot) eu<br> | |
| <br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="InputFile"></a> | |
| <hr> | |
| <center><b><font size="+2">Input File</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| A PRIMO input file is a text file (its syntax is similar to the one of Windows <b>ini</b> files) | |
| that should contain an integer to test. This integer should be greater than 65536 and less than | |
| 2^131072 (note that the greatest number ever certified with Primo is smaller than 2^28552).<br> | |
| The extension name of an input file should always be <b>.in</b>.<br> | |
| <br> | |
| <b><font size="+1">Syntax</font></b><br> | |
| <hr> | |
| An input file has syntax examplified by the text within the horizontal bars:<br> | |
| -------------------------------------------------------------------------------<br> | |
| <font color="#000099"> | |
| <b> | |
| ; any comment you want after a semi-colon<br> | |
| [Candidate]<br> | |
| N=<br> | |
| </b> | |
| </font> | |
| -------------------------------------------------------------------------------<br> | |
| The file may contain any number of blank lines.<br> | |
| <p> | |
| <b><u>Candidate expressed to the base 10</u></b><br> | |
| The number (or the expression) that follows <b><font color="#000099">N=</font></b> should be | |
| written on a single line.<br> | |
| There should be no character (Space, Tab, or else) before the first character of the section <b> | |
| <font color="#000099">[Candidate]</font></b>, before <b><font color="#000099">N=</font></b> or | |
| before a semicolon <b><font color="#000099">;</font></b><br> | |
| Expressions are allowed:<br> | |
| The alphabet is <b><font color="#000099">+ - * / ^ ! # ( ) 0 1 2 3 4 5 6 7 8 9</font></b><br> | |
| There should be NO SPACE in a number or before <b><font color="#000099">!</font></b> or | |
| <b><font color="#000099">#</font></b><br> | |
| Factorial(10) should be written <b><font color="#000099">10!</font></b><br> | |
| Primorial(13) should be written <b><font color="#000099">13#</font></b><br> | |
| <b><font color="#000099">!</font></b> also stands for Multi-Factorial, | |
| i.e., <b><font color="#000099">23!7 = 23*16*9*2</font></b>, in that case there should be NO SPACE | |
| before or after <b><font color="#000099">!</font></b><br> | |
| <b><font color="#000099">^</font></b> is associative on the left, | |
| i.e., <b><font color="#000099">a^b^c = (a^b)^c</font></b><br> | |
| <b><font color="#000099">N=10^999 + 7</font></b>, <b><font color="#000099">N=3229# + 1</font></b> | |
| or <b><font color="#000099">N= ((3229#) + 1)</font></b> are valid<br> | |
| <b><font color="#000099">N=32 29# + 1</font></b> is not valid, there is a space between two digits | |
| <p> | |
| <b><u>Candidate expressed to the base 16</u></b><br> | |
| To work with a number expressed to the base 16, use the key <b><font color="#000099">N$=</font></b> | |
| instead of <b><font color="#000099">N=</font></b><br> | |
| There should be no character (Space, Tab, or else) before the first character of the section | |
| <b><font color="#000099">[Candidate]</font></b>, before <b><font color="#000099">N=</font></b> or | |
| before a semicolon <b><font color="#000099">;</font></b><br> | |
| <b>Expressions are not allowed.</b><br> | |
| <hr><br> | |
| <br> | |
| <b><font size="+1">4 examples of valid input files</font></b><br> | |
| <hr> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| ;PRIMO Input File | |
| <p> | |
| [Candidate]<br> | |
| N=1384435372850622112932804334308326689651568940268408537 | |
| </font> | |
| </td> | |
| </tr> | |
| </table> | |
| <br> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| ;PRIMO Input File<br> | |
| ;Number expressed to the base 16 | |
| <p> | |
| [Candidate]<br> | |
| N$=cc8fa1481b11589c04f066367b204e09132082838aef805f207555505e690153 | |
| </font> | |
| </td> | |
| </tr> | |
| </table> | |
| <br> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| ;PRIMO Input File<br> | |
| ;This number will be rejected, it is less than 65536 | |
| <p> | |
| [Candidate]<br> | |
| N=997 | |
| </td> | |
| </tr> | |
| </table> | |
| <br> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| ;PRIMO Input File<br> | |
| ;Expression | |
| <p> | |
| [Candidate]<br> | |
| N=10^700 + 7 | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="OutputFile"></a> | |
| <hr> | |
| <center><b><font size="+2">Output File</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| A primality certificate is a sequence of integers that satisfy the requirements of various | |
| theorems (For more information concerning the tests used, see <a href="#Certificate">What | |
| is a primality certificate?</a>). With the primality certificate of an integer, an independent | |
| verifier can quickly check the primality of this integer.<br> | |
| Primality certificates are automatically saved to output files (which are text files), in the | |
| directory that contains the <a href="#InputFile">input file</a>.<br> | |
| <p> | |
| <b><font size="+1">Example of certificate</font></b><br> | |
| <hr> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| [PRIMO - Primality Certificate]<br> | |
| Version=3.0.9<br> | |
| WebSite=http://www.ellipsa.eu/<br> | |
| Format=3<br> | |
| ID=B2D6C052498F2<br> | |
| Created=12/25/2009 00:00:00 AM<br> | |
| TestCount=7<br> | |
| Status=Candidate certified prime | |
| <p> | |
| [Candidate]<br> | |
| File=C:\primo\work\first.in<br> | |
| N$=E74451F3DD74E0045407CF480C2A5DA72A57427444ED9<br> | |
| HexadecimalSize=45<br> | |
| DecimalSize=55<br> | |
| BinarySize=180 | |
| <p> | |
| [Running Times]<br> | |
| Initialization=0.00s<br> | |
| 1stPhase=0.01s<br> | |
| 2ndPhase=0.01s<br> | |
| Total=0.02s | |
| <p> | |
| [1]<br> | |
| Type=3<br> | |
| S$=30B73FD7A<br> | |
| R$=4BF4CBACF02AB9B134C2B4C499CC73301A5E9<br> | |
| A$=-1C4B8382FDCBBBEA5B211BD307615E17DD905ED42F69D<br> | |
| B$=0<br> | |
| T$=1 | |
| <p> | |
| [2]<br> | |
| Type=3<br> | |
| S$=12268EF<br> | |
| R$=42F4D55D4B18D2894579419DB0DB139<br> | |
| A$=-108<br> | |
| B$=69E<br> | |
| T$=2 | |
| <p> | |
| [3]<br> | |
| Type=1<br> | |
| S$=368E179DF8<br> | |
| R$=13A317FA2002F1E4803799<br> | |
| B$=2 | |
| <p> | |
| [4]<br> | |
| Type=1<br> | |
| S$=48<br> | |
| R$=45D21C5CE398B165561B<br> | |
| B$=2 | |
| <p> | |
| [5]<br> | |
| Type=3<br> | |
| S$=7D42A6<br> | |
| R$=8EB21868AEE181<br> | |
| A$=-1E<br> | |
| B$=38<br> | |
| T$=0 | |
| <p> | |
| [6]<br> | |
| Type=1<br> | |
| S$=20580<br> | |
| R$=4696ED2829<br> | |
| B$=2 | |
| <p> | |
| [7]<br> | |
| Type=0<br> | |
| <p> | |
| [Signature]<br> | |
| 1$=67B6BCF0700C92F36BBBD4CC32A1D9BD880323B4<br> | |
| 2$=1D845A7D5B774BCECDB5D70070BA063B991816F8 | |
| </font> | |
| </td> | |
| </tr> | |
| </table> | |
| Running time obtained with an AMD XP 3200+ processor<br> | |
| <hr><br> | |
| <b><font size="+1">Details</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=2 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="320"> | |
| <b><font face="Bitstream Vera Sans Mono">[PRIMO - Primality Certificate]</font></b> | |
| </td> | |
| <td> | |
| <b>Header section</b> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Version=</font> | |
| </td> | |
| <td> | |
| PRIMO version | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">WebSite=</font> | |
| </td> | |
| <td> | |
| Homepage of PRIMO | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Format=</font> | |
| </td> | |
| <td> | |
| Certificate format | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">ID=</font> | |
| </td> | |
| <td> | |
| Unique identifier that allows to know all files created during a given | |
| task (associated files always have the same identifier) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">Created=</font> | |
| </td> | |
| <td> | |
| Creation date of the certificate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">TestCount=</font> | |
| </td> | |
| <td> | |
| Total number of tests in the certificate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">Status=</font> | |
| </td> | |
| <td> | |
| Status of the certificate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td></td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font face="Bitstream Vera Sans Mono">[Candidate]</font></b> | |
| </td> | |
| <td> | |
| <b>Candidate section </b> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">File=</font> | |
| </td> | |
| <td> | |
| File name of the candidate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">Expression=</font> | |
| </td> | |
| <td> | |
| Candidate expressed as a formula (if any in the input file) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">N$=</font> | |
| </td> | |
| <td> | |
| Candidate (always expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">HexadecimalSize=</font> | |
| </td> | |
| <td> | |
| Hexadecimal size (base 16) of the candidate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">DecimalSize=</font> | |
| </td> | |
| <td> | |
| Decimal size (base 10) of the candidate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">BinarySize=</font> | |
| </td> | |
| <td> | |
| Binary size (base 2) of the candidate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td></td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font face="Bitstream Vera Sans Mono">[n]</font></b> | |
| </td> | |
| <td> | |
| <b>Test section </b><br> | |
| n is the number of the test | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Type=</font> | |
| </td> | |
| <td> | |
| Type of the test<br> | |
| 0: Strong pseudoprime<br> | |
| 1: N-1<br> | |
| 2: N+1<br> | |
| 3: Elliptic curve<br> | |
| 4: Elliptic curve | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">S$=</font> | |
| </td> | |
| <td> | |
| S (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">R$=</font> | |
| </td> | |
| <td> | |
| R (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">A$=</font> | |
| </td> | |
| <td> | |
| A (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">B$=</font> | |
| </td> | |
| <td> | |
| B (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">J$=</font> | |
| </td> | |
| <td> | |
| J (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">T$=</font> | |
| </td> | |
| <td> | |
| T (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">Q$=</font> | |
| </td> | |
| <td> | |
| Q (expressed to the base 16) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td></td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <b><font face="Bitstream Vera Sans Mono">[Signature]</font></b> | |
| </td> | |
| <td> | |
| <b>Signature section </b> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">1$=</font> | |
| </td> | |
| <td> | |
| 1st part of the signature of a certificate (160 bits) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">2$=</font> | |
| </td> | |
| <td> | |
| 2nd part of the signature of a certificate (160 bits) | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="TaskReportFile"></a> | |
| <hr> | |
| <center><b><font size="+2">Task Report File</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| After certifications or verifications, PRIMO opens the <a href="#TaskReportPage">Task | |
| Report Page</a> and displays miscellaneous information about the work done.<br> | |
| Task reports are automatically saved to <b>.tr</b> files. These text files are always created | |
| in the directory that contains the <a href="#InputFile">input files</a> (certifications) | |
| or the <a href="#OutputFile">output files</a> (verifications).<br> | |
| <p> | |
| <b><font size="+1">Example of task report file</font></b><br> | |
| <hr> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| [PRIMO - Task Report]<br> | |
| Version=3.0.9<br> | |
| WebSite=http://www.ellipsa.eu/<br> | |
| Task=Certification<br> | |
| ID=B2D6D00030D30<br> | |
| Created=12/25/2009 00:00:00 AM | |
| <p> | |
| [Common]<br> | |
| Path=C:\primo\bench\1024 bits\<br> | |
| Selected=3<br> | |
| Processed=3<br> | |
| Certified=3<br> | |
| Candidate #1=Certified, 5.72s<br> | |
| Candidate #2=Certified, 6.98s<br> | |
| Candidate #3=Certified, 6.60s | |
| <p> | |
| [Candidate #1]<br> | |
| Input=prime01.in<br> | |
| Output=Primo-B2D6D00030D30-001.out<br> | |
| Status=Candidate certified prime | |
| <p> | |
| [Candidate #2]<br> | |
| Input=prime02.in<br> | |
| Output=Primo-B2D6D00030D30-002.out<br> | |
| Status=Candidate certified prime | |
| <p> | |
| [Candidate #3]<br> | |
| Input=prime03.in<br> | |
| Output=Primo-B2D6D00030D30-003.out<br> | |
| Status=Candidate certified prime | |
| </font> | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="ReportFile"></a> | |
| <hr> | |
| <center><b><font size="+2">Report File</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| A certification report contains extra information regarding a certification.<br> | |
| Certification reports are saved to <b>.cr</b> files (which are text files), in the | |
| directory that contains the <a href="#InputFile">input files</a>.<br> | |
| <p> | |
| <b><font size="+1">Example of certification report</font></b><br> | |
| <hr> | |
| <table BORDER CELLPADDING=2 COLS=1 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono"> | |
| [PRIMO - Certification Report]<br> | |
| Version=3.0.9<br> | |
| ID=B2D6C052498F2<br> | |
| Created=12/25/2009 00:00:00 AM<br> | |
| Certificate=C:\primo\work\Primo-B2D6C052498F2-001.out<br> | |
| TestCount=7<br> | |
| <p> | |
| [Backtrack]<br> | |
| Count=0 | |
| <p> | |
| [1]<br> | |
| Type=3<br> | |
| Run=1<br> | |
| Gain=33<br> | |
| D=-4<br> | |
| H=1<br> | |
| G=1 | |
| <p> | |
| [2]<br> | |
| Type=3<br> | |
| Run=1<br> | |
| Gain=24<br> | |
| D=-11<br> | |
| H=1<br> | |
| G=1 | |
| <p> | |
| [3]<br> | |
| Type=1<br> | |
| Run=1<br> | |
| Gain=38 | |
| <p> | |
| [4]<br> | |
| Type=1<br> | |
| Run=1<br> | |
| Gain=6 | |
| <p> | |
| [5]<br> | |
| Type=3<br> | |
| Run=1<br> | |
| Gain=23<br> | |
| D=-8<br> | |
| H=1<br> | |
| G=1 | |
| <p> | |
| [6]<br> | |
| Type=1<br> | |
| Run=1<br> | |
| Gain=17<br> | |
| <p> | |
| [7]<br> | |
| Type=0<br> | |
| Run=1<br> | |
| Gain=39 | |
| </font> | |
| </td> | |
| </tr> | |
| </table> | |
| <br> | |
| <b><font size="+1">Details</font></b><br> | |
| <hr> | |
| <table BORDER=0 CELLPADDING=4 WIDTH="100%" BGCOLOR="#F7F7F7"> | |
| <tr> | |
| <td VALIGN=TOP WIDTH="300"> | |
| <b><font face="Bitstream Vera Sans Mono">[PRIMO - Certification Report]</font></b> | |
| </td> | |
| <td> | |
| <b>Header section</b> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Version=</font> | |
| </td> | |
| <td> | |
| PRIMO version | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">WebSite=</font> | |
| </td> | |
| <td> | |
| Home page of PRIMO | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">ID=</font> | |
| </td> | |
| <td> | |
| Unique identifier that allows to know all files created during a given | |
| task (Associated files always have the same identifier) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">Created=</font> | |
| </td> | |
| <td> | |
| Creation date of the certificate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Certificate=</font> | |
| </td> | |
| <td> | |
| Filename of the certificate associated with the report | |
| </td> | |
| </tr> | |
| <tr> | |
| <td> | |
| <font face="Bitstream Vera Sans Mono">TestCount=</font> | |
| </td> | |
| <td> | |
| Total number of tests in the certificate | |
| </td> | |
| </tr> | |
| <tr> | |
| <td></td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font face="Bitstream Vera Sans Mono">[Backtrack]</font></b> | |
| </td> | |
| <td> | |
| <b>Bactrack section </b><br> | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Count=</font> | |
| </td> | |
| <td> | |
| Total number of backtracked tests | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Rejected=</font> | |
| </td> | |
| <td> | |
| List of the backtracked tests | |
| </td> | |
| </tr> | |
| <tr> | |
| <td></td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <b><font face="Bitstream Vera Sans Mono">[n] or [n (backtracked:m)]</font></b> | |
| </td> | |
| <td> | |
| <b>Test section </b><br> | |
| n is the number of the test<br> | |
| m is the number of times the test n was backtracked | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Type=</font> | |
| </td> | |
| <td> | |
| Type of the test<br> | |
| 0: Strong pseudoprime<br> | |
| 1: N-1<br> | |
| 2: N+1<br> | |
| 3: Elliptic curve<br> | |
| 4: Elliptic curve | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Run=</font> | |
| </td> | |
| <td> | |
| Run on which the test was found (during Phase 1) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">Gain=</font> | |
| </td> | |
| <td> | |
| Gain = BitSize(N) - BitSize(R) except for the last test where Gain = BitSize(N)<br> | |
| The N value of a test is equal to the R value of the preceding test (or to the | |
| candidate for the first test) | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">D=</font> | |
| </td> | |
| <td> | |
| Discriminant used for the test | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">H=</font> | |
| </td> | |
| <td> | |
| Class number associated with the discriminant D | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">G=</font> | |
| </td> | |
| <td> | |
| Genus number associated with the discriminant D<br> | |
| PRIMO has to factor a polynomial of which the degree is at most H/G | |
| </td> | |
| </tr> | |
| <tr> | |
| <td VALIGN=TOP> | |
| <font face="Bitstream Vera Sans Mono">R$=</font> | |
| </td> | |
| <td> | |
| Backtracked tests only<br> | |
| R (expressed to the base 16) is the value with which PRIMO failed to complete a test | |
| </td> | |
| </tr> | |
| </table> | |
| <hr><br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <a NAME="License"></a> | |
| <hr> | |
| <center><b><font size="+2">License</font></b></center> | |
| <hr><br> | |
| <blockquote> | |
| PRIMO - Primality Proving. Copyright © 2007, Marcel Martin. All rights reserved. | |
| <p> | |
| By installing and/or using the software PRIMO (the "Software"), you (the "User") (either | |
| on behalf of yourself as an individual or on behalf of an entity as its authorized | |
| representative) agree to all of the terms of this end-user license agreement (the | |
| "Agreement") regarding your use of the Software and you also agree that this is the entire | |
| agreement between the author (the "Author") of the Software and you, which supersedes any | |
| prior agreement, whether written or oral, and all other communications between the Author | |
| and you relating to the subject matter of this Agreement. | |
| <p> | |
| <b>GRANT OF LICENSE</b><br> | |
| Subject to the terms below, the Author hereby grants the User a non-exclusive, non-transferable | |
| license to install and to use the Software. | |
| <p> | |
| <b>DISCLAIMER OF WARRANTY</b><br> | |
| The Software and its documentation are provided "as is" without warranty of any kind.<br> | |
| The Author makes no representations or warranties about the suitability of the Software, | |
| either express or implied, including but not limited to the implied warranties of | |
| merchantability, fitness for a particular purpose, or non-infringement.<br> | |
| If the User of this Software deems it unsuitable for any particular purpose, the User's | |
| sole remedy shall be to refrain from using it.<br> | |
| The Author shall not be liable for any damages suffered by the User as a result of using, | |
| modifying or distributing the Software, including direct, indirect, incidental, consequential | |
| or other damages, even if the Author has been advised of the possibility of such damages. | |
| <p> | |
| <b>INTELLECTUAL PROPERTY</b><br> | |
| No title to the intellectual property in the Software is transferred to the User. Title, | |
| ownership, rights, and intellectual property rights in and to the Software shall remain to the | |
| Author. | |
| <p> | |
| <b>TERMINATION</b><br> | |
| This Agreement shall terminate automatically if the User fails to comply with the limitations | |
| described in this Agreement. No notice shall be required from the Author to effectuate such | |
| termination. Upon termination, the User must uninstall and destroy all copies of the Software. | |
| <p> | |
| <b>GOVERNING LAWS</b><br> | |
| This Agreement shall be governed by the laws of France. | |
| <p> | |
| <b>PATENTS</b><br> | |
| If the Author is advised that the Software is infringing a patent, the Author shall forbid | |
| distribution and use of the Software in all countries where the patent is applicable. In this | |
| case, the User's sole remedy shall be to refrain from using the Software in such countries. | |
| <p> | |
| <b>SEVERABILITY</b><br> | |
| In the event of invalidity of any provision of this Agreement, the Author and the User | |
| agree that such invalidity shall not affect the validity of the remaining portions of this | |
| Agreement. | |
| <p> | |
| <b>RESERVATION OF RIGHTS</b><br> | |
| All rights not expressly granted in this Agreement are reserved by the Author. | |
| <p> | |
| <i>June 21, 2007</i><br> | |
| <i>Colombes, France</i><br> | |
| <br> | |
| <a href="#Contents">Contents</a><br> | |
| </blockquote> | |
| <br> | |
| <br> | |
| <p> | |
| <hr> | |
| <center> | |
| <font size="-1"> | |
| Copyright © 2009, Marcel Martin<br> | |
| <a href="http://www.ellipsa.eu/index.html">http://www.ellipsa.eu/index.html</a><br> | |
| </font> | |
| </center> | |
| </font> | |
| </body> | |
| </html> |