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<head>
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<title>PRIMO - Primality Proving</title>
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<body>
<div><a name="Contents"></a></div>
<h1>PRIMO - Primality Proving</h1>
<p><br /></p>
<h2>Contents</h2>
<p><br /></p>
<table class="contents">
<tr>
<td>
<ul>
<li class="li1">Manual
<ul>
<li><a href="#Overview">Overview</a></li>
<ul>
<li class="li2"><a href="#OverviewWhatisPRIMO">What is PRIMO?</a></li>
<li class="li2"><a href="#OverviewLatestRelease">Latest Release</a></li>
<li class="li2"><a href="#OverviewContact">Contact</a></li>
</ul>
<li><a href="#GettingStarted">Getting started</a></li>
<ul>
<li class="li2"><a href="#GettingStartedTextFiles">Text Files</a></li>
<li class="li2"><a href="#GettingStartedGoodPractice">Good Practice</a></li>
<li class="li2"><a href="#GettingStartedFirstSession">First Session</a></li>
</ul>
<li><a href="#Menu">Menu</a></li>
<ul>
<li class="li2"><a href="#MenuItems">Items</a></li>
</ul>
<li><a href="#SetupBox">Setup dialog box</a></li>
<ul>
<li class="li2"><a href="#SetupBoxComponents">Components</a></li>
</ul>
<li><a href="#WorkReportPage">Work Report page</a></li>
<ul>
<li class="li2"><a href="#WorkReportPageReportEditor">Report Editor</a></li>
</ul>
<li><a href="#CertificationPage">Certification page</a></li>
<ul>
<li class="li2"><a href="#CertificationPageSetup">Setup</a></li>
<li class="li2"><a href="#CertificationPageStatus">Status</a></li>
<li class="li2"><a href="#CertificationPageButtons">Buttons</a></li>
</ul>
<li><a href="#VerificationPage">Verification page</a></li>
<ul>
<li class="li2"><a href="#VerificationPageSetup">Setup</a></li>
<li class="li2"><a href="#VerificationPageStatus">Status</a></li>
<li class="li2"><a href="#VerificationPageButtons">Buttons</a></li>
</ul>
</ul>
</li>
</ul>
</td>
<td>
<ul>
<li class="li1">Files
<ul>
<li><a href="#InputFile">Input (Candidate)</a></li>
<ul>
<li class="li2"><a href="#InputFileExamples">Examples of valid input files</a></li>
</ul>
<li><a href="#OutputFile">OutPut (Certificate)</a></li>
<ul>
<li class="li2"><a href="#OutputFileExample">Example of certificate</a></li>
<li class="li2"><a href="#OutputFileDetails">Details</a></li>
</ul>
<li><a href="#WorkReportFile">Work Report</a></li>
<ul>
<li class="li2"><a href="#WorkReportFileExample">Example of work report</a></li>
</ul>
<!--
<li><a href="#CertificationReportFile">Certification Report</a></li>
<ul>
<li class="li2"><a href="#CertificationReportFileExample">Example of certification report</a></li>
<li class="li2"><a href="#CertificationReportFileDetails">Details</a></li>
</ul>
-->
</ul>
</li>
</ul>
<ul>
<li class="li1">Miscellaneous
<ul>
<li><a href="#Resuming">How to resume a certification?</a></li>
<li><a href="#InternalError">Internal Error</a></li>
<li><a href="#License">End-User License</a></li>
</ul>
</li>
</ul>
</td>
</tr>
</table>
<p><br /></p>
<div><a name="Overview"></a></div>
<p><br /></p>
<h2>Overview</h2>
<div><a name="OverviewWhatisPRIMO"></a></div>
<h3>What is PRIMO?</h3>
<p class="jtext">
PRIMO is a primality proving program based on the ECPP (Elliptic Curve Primality Proving)
algorithm. Given positive odd integers, PRIMO tests whether these integers are prime, and if
they are it produces <a href="#OutputFile">primality certificates</a>.<br />
PRIMO is suitable for the checking of crypto-primes and to prove whether they are actually
prime... or not.
</p>
<div><a name="OverviewLatestRelease"></a></div>
<h3>Latest Release</h3>
<p class="jtext">
In order to check whether you have the most recent version of PRIMO, please, visit the
<a href="http://www.ellipsa.eu/index.html">PRIMO Homepage</a>.
</p>
<div><a name="OverviewContact"></a></div>
<h3>Contact</h3>
<p class="jtext">
In order to send any comment, suggestion, bug report, whatever, see the
<a href="http://www.ellipsa.eu/public/misc/contact.html">PRIMO contact page</a>.
</p>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="GettingStarted"></a></div>
<p><br /></p>
<h2>Getting Started</h2>
<div><a name="GettingStartedTextFiles"></a></div>
<h3>Text Files</h3>
<p class="jtext">
When running, PRIMO works with the following text files:<br />
<span class="mono">*.in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>
<a href="#InputFile">Input file</a> (Integer to test)<br />
<span class="mono">primo-xxxxxxxxxxxxxxx-nnn.out&nbsp;&nbsp;</span>
<a href="#OutputFile">Output file</a> (Primality certificate)<br />
<span class="mono">primo-xxxxxxxxxxxxxxx.wr&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>
<a href="#WorkReportFile">Work Report file</a><br />
<span class="mono">xx..xx</span>
is a unique hexadecimal number that allows to identify all the files created during batch processing.<br />
<span class="mono">nnn</span> is an hexadecimal number
that indicates the index (when batch processing only) of the tested integer.<br />
</p>
<div><a name="GettingStartedGoodPractice"></a></div>
<h3>Good Practice</h3>
<p class="jtext">
In order to certify a number, always create a directory and copy the input file in this
directory. Doing so, all the files related to the certification will be located in this
directory (while certifying, depending on the size of the number, PRIMO can create hundreds,
and even thousands, of temporary files).
</p>
<div><a name="GettingStartedFirstSession"></a></div>
<h3>First Session</h3>
<ul>
<li>Run PRIMO.</li>
<li>Open the menu.</li>
<li>Click on the <i>New input file...</i> item.</li>
<li>Create the <i>new.in</i> file (once created, this file is displayed in a text editor).</li>
<li>Write "10^55 + 21" (only the number not the quotes) after "N=".</li>
<li>Save the file and close the text editor.</li>
<li>Select the <i>Certification</i> tab.</li>
<li>Select "2000 dd" with the <i>Number size</i> button.</li>
<li>Select "23 bits" with the <i>Divisor size</i> button.</li>
<li>Click on the <i>Build prime table</i> button.</li>
<li>Click on the <i>Load</i> button.</li>
<li>Double-click on <i>new.in</i>.</li>
</ul>
<p class="jtext">
When the certification is done, a short report is displayed in the editor of the
<a href="#WorkReportPage">Work Report page</a>. To open a results text
file, double-click on the relevant item.
</p>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="Menu"></a></div>
<p><br /></p>
<h2>Menu</h2>
<div><a name="MenuItems"></a></div>
<h3>Items</h3>
<table class="details">
<tr>
<td class="f1">New input file...</td>
<td>Create a new empty <a href="#InputFile">input file</a>.</td>
</tr>
<tr>
<td class="f1">Open a Primo text file...</td>
<td>Open a file list box with which you can select PRIMO text files: input,
<a href="#OutputFile">output</a> and <a href="#WorkReportFile">work report</a>.
These files are open with the text editor you associated with their extensions.
</td>
</tr>
<tr>
<td class="f1">Setup...</td>
<td>
Open the <a href="#SetupBox"> Setup dialog box</a>.<br />
</td>
</tr>
<tr>
<td class="f1">Open the help file...</td>
<td>Open the documentation.</td>
</tr>
<tr>
<td class="f1">About...</td>
<td>Open the About dialog box.</td>
</tr>
<tr>
<td class="f1">Quit</td>
<td class="last">Close PRIMO.</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="SetupBox"></a></div>
<p><br /></p>
<h2>Setup dialog box</h2>
<div><a name="SetupBoxComponents"></a></div>
<h3>CPU Info</h3>
<table class="details">
<tr>
</tr>
<tr>
<td class="f1">CPU Info</td>
<td class="last">
This group box indicates
<ul>
<li>the name of the processors (in case there are more than one processor on a
motherboard, it is assumed they are all identical);</li><br />
<li>the number of physical processors on the motherboard, the number of cores per processor,
and the number of hyperthreads per core.</li>
</ul>
</td>
</tr>
</table>
<h3>Common</h3>
<table class="details">
<tr>
</tr>
<tr>
<td class="f1">Concurrent tasks...</td>
<td>
Max number of concurrent tasks.<br />
<br />
The value should be chosen according to the number of processors, the number of
cores per processor and the number of hyperthreads per core.<br />
For instance, with one processor, four cores per processor and two hyperthreads
per core, one could select up to 1*4*2 = 8 tasks.<br />
</td>
</tr>
<tr>
<td class="f1">Hexadecimal strings...</td>
<td>
Generate hexadecimal strings prefixed with '0x' instead of '$'.<br />
<br />
If checked the Pascal hexadecimal tag '$' is replaced with '0x' in certificates.
Primo can work (reading/writing) with text files using both tags.<br />
<br />
<i>Default value = Unchecked</i>
</td>
</tr>
<tr>
<td class="f1">Reset button</td>
<td class="last">
This button allows to reset the default value.
</td>
</tr>
</table>
<h3>Phase 1</h3>
<table class="details">
<tr>
</tr>
<tr>
<td class="f1">Min binary gain<br /></td>
<td>
This parameter allows to increase or to decrease the minimal gain of a test during the pass #1.<br />
<br />
This parameter has no effect during the first test of a certification.<br />
<br />
<i>Default value = 100%</i>
</td>
</tr>
<tr>
<td class="f1">Elliptic curve tests only<br /></td>
<td>
If checked, the produced primality certificates contain no <i>N+/-1</i> tests.<br />
<br />
<i>Default value = Unchecked</i>
</td>
</tr>
<tr>
<td class="f1">Backtrack<br />Never before...</td>
<td>
Primo does not try to backtrack before having run the discriminant table whose number is
specified.<br />
<br />
This directive has no effect during the first test of a certification.<br />
<br />
<i>Default value = 2</i>
</td>
</tr>
<tr>
<td class="f1">Backtrack<br />Always after...</td>
<td>
Primo always tries to backtrack after having run the discriminant table whose number is
specified.<br />
<br />
This directive has no effect during the first test of a certification.<br />
<br />
<i>Default value = 22</i>
</td>
</tr>
<tr>
<td class="f1">Reset button</td>
<td class="last">
This button allows to reset the default values.
</td>
</tr>
</table>
<h3>Verification</h3>
<table class="details">
<tr>
</tr>
<tr>
<td class="f1">Obsolete tests...</td>
<td>
Suppress obsolete tests, if any, when updating certificates.<br />
<br />
Due to the new final test of format-4 certificates, when updating certificates from format-3 to
format-4, the very last test(s) of a format-3 certificate may be suppressed.<br />
<br />
If checked, the obsolete tests are suppressed from the updated certificates.<br />
<br />
<i>Default value = Checked</i>
</td>
</tr>
<tr>
<td class="f1">Reset button</td>
<td class="last">
This button allows to reset the default value.
</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="WorkReportPage"></a></div>
<p><br /></p>
<h2>Work Report Page</h2>
<p class="jtext">
The Work Report page contains an editor used to display certification and verification reports.
</p>
<div><a name="WorkReportPageReportEditor"></a></div>
<h3>Report Editor</h3>
<p class="jtext">
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="#WorkReportFile">work
report file</a> (text file).
</p>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="CertificationPage"></a></div>
<p><br /></p>
<h2>Certification Page</h2>
<p class="jtext">
The Certification page allows to perform the certification of
integers in PRIMO <a href="#InputFile">input files</a> and also to resume
aborted certificates:<br />
- loading <b>.in</b> files starts certifications ;<br />
- loading <b>.tmp</b> files restarts aborted certifications.<br />
<br />
The certificates are always 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.
Do not modify them. If ever a <b>.tmp</b> file is modified, all the work done could be lost!<br />
<br />
During a certification, the work in progress is automatically saved every 10 minutes.<br />
<br />
See also: <a href="#OutputFile">Primality certificate</a>
</p>
<div><a name="CertificationPageSetup"></a></div>
<h3>Setup</h3>
<table class="details">
</tr>
<tr>
<td class="f1">Trial division parameters</td>
<td>
In order to factor elliptic curve orders, one has to select 2 parameters:
<ul>
<li>
<i>Number Size (NS)</i><br />
Decimal size of a number to test.<br /><br />
</li>
<li>
<i>Divisor Size (DS)</i><br />
Maximal binary size of the prime divisors used by Primo.
</li>
</ul>
When certifying,
<ul>
<li>if the decimal size of a number to test (a candidate or a N value of a
certificate test) is greater than or equal to <i>NS</i>, the maximal binary size of
the divisors is constant and equal to <i>DS</i> (i.e., Primo makes use of all small
primes <i>p</i> such that <i>p < 2<sup>DS</sup></i>);<br /><br /></li>
<li>while the decimal size of a number to test decreases from <i>NS</i> downto 1000,
the maximal binary size of the divisors linearly decreases from <i>DS</i> downto
22;<br /><br /></li>
<li>if the decimal size of a number to test is less than 1000, Primo makes use of
internal parameters that cannot be modified.</li>
</ul>
To modify the values, use the arrow keys or click on the buttons and select new values in
the menus.<br />
<br />
When the NS value is modified, the DS value is automatically set to the default value
associated with the new NS value (like indicated in the following table).
So, one should always set the <i>NS</i> before setting the <i>DS</i>.<br />
<br />
<table border="1" cellspacing="0">
<tr><th>&nbsp;Number Size&nbsp;</th><th>&nbsp;Divisor Size&nbsp;</th></tr>
<tr><td align="right">2000 decimal digits&nbsp;</td><td align="center">23 bits</td></tr>
<tr><td align="right">3000 decimal digits&nbsp;</td><td align="center">24 bits</td></tr>
<tr><td align="right">4000 decimal digits&nbsp;</td><td align="center">25 bits</td></tr>
<tr><td align="right">5000 decimal digits&nbsp;</td><td align="center">26 bits</td></tr>
<tr><td align="right">6000 decimal digits&nbsp;</td><td align="center">27 bits</td></tr>
<tr><td align="right">7000 decimal digits&nbsp;</td><td align="center">28 bits</td></tr>
<tr><td align="right">8000 decimal digits&nbsp;</td><td align="center">29 bits</td></tr>
<tr><td align="right">9000 decimal digits&nbsp;</td><td align="center">30 bits</td></tr>
<tr><td align="right">10000 decimal digits&nbsp;</td><td align="center">31 bits</td></tr>
<tr><td align="right">11000 decimal digits&nbsp;</td><td align="center">32 bits</td></tr>
<tr><td align="right">beyond&nbsp;</td><td align="center">32 bits</td></tr>
</table>
<br />
</td>
</tr>
<tr>
<td class="f1">Build prime table</td>
<td class="last">
Create a prime table containing all the primes having a binary size smaller than or equal to
<i>Divisor Size</i>.<br />
It might be necessary to increase the Linux <i>kernel.shmmax</i> value. With Ubuntu, one can do
it using the following command line (after having replaced <span class="mono"><b>newsize</b></span>
with the value indicated in the PRIMO status line):<br />
<br />
<span class="mono">sudo sh -c 'echo <b>newsize</b> &gt; /proc/sys/kernel/shmmax'</span><br />
<br />
This modification will last until Linux is rebooted.
</td>
</tr>
</table>
<div><a name="CertificationPageStatus"></a></div>
<h3>Status</h3>
<table class="details">
<tr>
<td class="f1">Elapsed time</td>
<td>Running time of the certification.</td>
</tr>
<tr>
<td class="f1">Number</td>
<td>Number (in the input file list) of the integer that is currently tested.</td>
</tr>
<tr>
<td class="f1">Phase</td>
<td>
Number of the current phase (1 or 2).<br />
<br />
The <i>Phase 1</i> consists in finding a list of primes.<br />
<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 list of primes found
during the <i>Phase 1</i> is indeed a list of primes).
</td>
</tr>
<tr>
<td class="f1">Test</td>
<td>Number of the current test.<br />The value may decrease due to backtracking.</td>
</tr>
<tr>
<td class="f1">Bits</td>
<td>Indicates the binary size of the integer currently tested.</td>
</tr>
<tr>
<td class="f1">1..48</td>
<td class="last">Miscellaneous information regarding the current status of a certification (each task has
its own status line).</td>
</tr>
</table>
</p>
<div><a name="CertificationPageButtons"></a></div>
<h3>Buttons</h3>
<table class="details">
<tr>
<td class="f1">Load</td>
<td>
Load files (up to 4095 files) and start certifications (and/or restart aborted certifications). The
selected files are always processed in alphabetical order.
</td>
</tr>
<tr>
<td class="f1">Abort</td>
<td class="last">
Allow to abort a certification.<br />
<br />
When a certification is aborted, data that allow to resume it are saved to a file having
the <b>.tmp</b> extension. To restart the certification, just load this file.
</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="VerificationPage"></a></div>
<p><br /></p>
<h2>Verification Page</h2>
<p class="jtext">
The Verification page allows to verify and to sign certificates (format-3 and/or format-4).
Note that the certificates are always verified and signed while certifying.<br />
<br />
When signing, the work in progress is automatically saved every 10 minutes.<br />
<br />
See also: <a href="#OutputFile">Primality certificate</a>
</p>
<div><a name="VerificationPageSetup"></a></div>
<h3>Setup</h3>
<table class="details">
<tr>
<td class="f1">Check signatures only</td>
<td>
If 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 />
<br />
If not checked, PRIMO always verifies the certificate and signs it.<br />
<br />
<i>Default value = Checked</i>
</td>
</tr>
<tr>
<td class="f1">Update certificates</td>
<td class="last">
If checked, PRIMO tries to update an old format-3 certificate to format-4.<br />
<br />
If the format-3 certificate is signed and if the <i>Check signatures only</i> option is checked, the
creation of the format-4 certificate is very fast.<br />
<br />
If the format-3 certificate is not signed or if the <i>Check signatures only</i> option is not checked,
PRIMO performs a full verification before creating the format-4 certificate.<br />
<br />
<i>Default value = Unchecked</i>
</td>
</tr>
</table>
<div><a name="VerificationPageStatus"></a></div>
<h3>Status</h3>
<table class="details">
<tr>
<td class="f1">Elapsed time</td>
<td>Running time of the verification.</td>
</tr>
<tr>
<td class="f1">Certificate</td>
<td>
Number (in the <a href="#OutputFile">output file</a> list) of the certificate that is currently verified.
</td>
</tr>
<tr>
<td class="f1">Test</td>
<td>Number of the current test.</td>
</tr>
<tr>
<td class="f1">Bits</td>
<td>Indicates the binary size of the integer currently checked.</td>
</tr>
<tr>
<td class="f1">1..48</td>
<td class="last">Miscellaneous information regarding the current status of a verification (each
task has its own status line).</td>
</tr>
</table>
<div><a name="VerificationPageButtons"></a></div>
<h3>Buttons</h3>
<table class="details">
<tr>
<td class="f1">Load</td>
<td>
Load files (up to 4095 files) and start verifications. The selected files are always processed in
alphabetical order.
</td>
</tr>
<tr>
<td class="f1">Abort</td>
<td class="last">
Abort a verification.<br />
<br />
In order to resume an aborted verification, just reload the <b>.out</b> file.
</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="Resuming"></a></div>
<p><br /></p>
<h2>How to resume a certification?</h2>
<div class="jtext">
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 />
That's all.
</div>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="InputFile"></a></div>
<p><br /></p>
<h2>Input File</h2>
<div class="jtext">
A PRIMO input file is a text file that should contain an integer to test. This integer should be greater
than 1 and less than 2<sup>166016</sup> (i.e. a little more than 50000 decimal digits).<br />
<br />
The extension name of an input file must always be <b>.in</b>.<br />
<br />
An input file has a syntax examplified by the text within the horizontal bars:<br />
<span class="monoblue">
-----------------------------------------<br />
; any comment you want after a semi-colon<br />
[Candidate]<br />
N=<br />
-----------------------------------------<br />
</span>
The file may contain any number of blank lines.<br />
The number (or the expression) that follows <span class="monoblue">N=</span> must be
written on a single line.<br />
There must be no character (Space, Tab, or else) before the first character of the section
<span class="monoblue">[Candidate]</span>, before <span class="monoblue">N=</span> or
before a semicolon <span class="monoblue">;</span><br />
Expressions are allowed.<br />
<br />
<table border="1" cellspacing="0" cellpadding="4">
<tr>
<td><b>Symbol</b>&nbsp;&nbsp;</td><td><b>Meaning</b>&nbsp;&nbsp;</td><td><b>Comment</b></td>
</tr>
<tr>
<td><span class="monoblue">+</span></td>
<td>Addition</td>
<td>There is no unary <span class="monoblue">+</span></td>
</tr>
<tr>
<td><span class="monoblue">-</span></td>
<td>Subtraction</td>
<td>There is no unary - (but if need be it can be coded as <span class="monoblue">(0-n)</span>)</td>
</tr>
<tr>
<td><span class="monoblue">*</span></td>
<td>Multiplication</td>
<td></td>
</tr>
<tr>
<td><span class="monoblue">/</span></td>
<td>Division</td>
<td>Integer division<br />
Example: <span class="monoblue">8/3</span> is equal to 2 (not to 2.66666...)</td>
</tr>
<tr>
<td><span class="monoblue">^</span><br /><span class="monoblue">**</span></td>
<td>Exponentiation</td>
<td>The exponentiation is associative on the left: <span class="monoblue">a^b^c = (a^b)^c</span>&nbsp;</td>
</tr>
<tr>
<td><span class="monoblue">!</span></td>
<td>Factorial</td>
<td>Example: <span class="monoblue">7!</span> is equal to 7*6*5*4*3*2<br />
Spaces before the symbol <span class="monoblue">!</span> are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">!!</span></td>
<td>Multi-factorial</td>
<td>Example: <span class="monoblue">23!!7</span> is equal to 23*16*9*2<br />
Spaces before or after the symbols <span class="monoblue">!</span> are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">#</span></td>
<td>Primorial</td>
<td><span class="monoblue">n#</span> is the product of all the primes less than or equal to n<br />
Spaces before the symbol <span class="monoblue">#</span> are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">$</span><br /><span class="monoblue">0x</span></td>
<td>Base-16 prefixes</td>
<td>Example: <span class="monoblue">$2bc</span> or <span class="monoblue">0x2bc</span> are equal to 700<br />
Spaces between the prefix and the first digit are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">0..9</span></td>
<td>Base-10 digits</td>
<td>Spaces between the digits of a number are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">0..9</span><br /><span class="monoblue">a..f</span><br /><span class="monoblue">A..F</span></td>
<td>Base-16 digits</td>
<td>Spaces between the digits of a number are not allowed</td>
</tr>
<tr>
<td><span class="monoblue">(</span></td>
<td>Opening bracket&nbsp;&nbsp;</td>
<td></td>
</tr>
<tr>
<td><span class="monoblue">)</span></td>
<td>Closing bracket</td>
<td></td>
</tr>
</table>
</div>
<br />
In case of error when evaluating an expression, Primo reports either the position of the first invalid
symbol or one of the following error codes.<br />
<br />
<table border="1" cellspacing="0" cellpadding="4">
<tr><td><b>Code</b>&nbsp;&nbsp;&nbsp;</td><td><b>Meaning</b></td></tr>
<tr><td>-1</td><td>An exception occurred (user abort, system, ...)</td></tr>
<tr><td>-2</td><td>Invalid expression</td></tr>
<tr><td>-3</td><td>The number of closing brackets is not equal to the number of opening ones&nbsp;</td></tr>
<tr><td>-4</td><td>Invalid factorial operand (op > 65535)</td></tr>
<tr><td>-5</td><td>Invalid multi-factorial operands ((op1 < op2) or (op1 &ge; 2<sup>64</sup>) or (op2 < 1))</td></tr>
<tr><td>-6</td><td>Invalid primorial operand ((op < 2) or (op > 65521))</td></tr>
<tr><td>-7</td><td>Division by 0</td></tr>
<tr><td>-8</td><td>Overflow: an intermediate result became greater than or equal to 2<sup>531456</sup></td></tr>
</table>
</div>
<p><br /></p>
<div><a name="InputFileExamples"></a></div>
<h3>Examples of valid input files</h3>
<p></p>
<table class="code">
<tr>
<td>
;PRIMO Input File<br />
<br />
[Candidate]<br />
N=1384435372850622112932804334308326689651568940268408537
</td>
</tr>
</table>
<p></p>
<table class="code">
<tr>
<td>
;PRIMO Input File<br />
;Number expressed to the base 16<br />
<br />
[Candidate]<br />
N=$cc8fa1481b11589c04f066367b204e09132082838aef805f207555505e690153
</td>
</tr>
</table>
<p></p>
<table class="code">
<tr>
<td>
;PRIMO Input File<br />
;Expression<br />
<br />
[Candidate]<br />
N=10^700 + 7
</td>
</tr>
</table>
<p></p>
<table class="code">
<tr>
<td>
;PRIMO Input File<br />
;Expression with integers expressed to the base 16 (equivalent to 10^700 + 7)<br />
<br />
[Candidate]<br />
N=$A^$2BC + $7
</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="OutputFile"></a></div>
<p><br /></p>
<h2>Output File (Certificate)</h2>
<div class="jtext">
A primality certificate is a sequence of integers that satisfy the requirements of various
theorems. With the primality certificate of an integer, an independent verifier can quickly
check the primality of this integer (in order to write a verifier, see the <b>verifier-f4.txt</b> file).<br />
<br />
Primality certificates are automatically saved to output files (which ones are text files),
in the directory that contains the <a href="#InputFile">input file</a>.
</div>
<div><a name="OutputFileExample"></a></div>
<h3>Example of certificate</h3>
<p></p>
<table class="code">
<tr>
<td>
[PRIMO - Primality Certificate]<br />
Version=x.x.x - LX64<br />
WebSite=http://www.ellipsa.eu/<br />
Format=4<br />
ID=B346B00DD802B<br />
Created=???-00-0000 00:00:00 AM<br />
TestCount=7<br />
Status=Candidate certified prime<br />
<br />
[Comments]<br />
Put here any comment...<br />
<br />
[Running Times (Wall-Clock)]<br />
1stPhase=0.02s<br />
2ndPhase=0.01s<br />
Total=0.03s<br />
<br />
[Running Times (Processes)]<br />
1stPhase=0.03s<br />
2ndPhase=0.01s<br />
Total=0.04s<br />
<br />
[Candidate]<br />
File=/home/lx64/work/new.in<br />
Expression=10^55+21<br />
N=$6867A5A867F103B2FFFA5A71FBA0E7B680000000000015<br />
HexadecimalSize=46<br />
DecimalSize=56<br />
BinarySize=183<br />
<br />
[1]<br />
S=$2<br />
W=-$144534B5B2A8FE0395A5EE94<br />
A=-$3433D2D433F881D97FFD2D38FDD073DB4000000000000A<br />
B=0<br />
T=$2<br />
<br />
[2]<br />
S=$8<br />
W=-$B6EBCBCA04B86F63A8D2612<br />
A=-$1<br />
B=0<br />
T=$2<br />
<br />
[3]<br />
S=$6258F9<br />
W=-$23F79D321EF79576E0D7D1<br />
A=-$108<br />
B=$69E<br />
T=$1<br />
<br />
[4]<br />
S=$D766<br />
B=$2<br />
<br />
[5]<br />
S=$166E14C9BA<br />
W=$777E21A2ED19AA5FD0<br />
A=$6BAA29FD34D420C1E9A55D6959BD90CF0FE<br />
B=0<br />
T=$2<br />
<br />
[6]<br />
S=$F432<br />
Q=$6<br />
<br />
[7]<br />
S=$155EC18050<br />
W=$11255F5B55E6<br />
A=-$108<br />
B=$69E<br />
T=$1<br />
<br />
[Signature]<br />
1=$8817CEEE51DDDF518A14AA0DB012940266AA9D0D39323778<br />
2=$1DD92A5916A0F532586ABCF17F005AC870CAE0F9E4B146A9
</td>
</tr>
</table>
<div><a name="OutputFileDetails"></a></div>
<h3>Details</h3>
<table class="details">
<tr>
<td class="f2">[PRIMO - Primality Certificate]</td>
<td><b>Header section</b></td>
</tr>
<tr>
<td class="f2">Version=</td>
<td>PRIMO version</td>
</tr>
<tr>
<td class="f2">Website=</td>
<td>Homepage of PRIMO</td>
</tr>
<tr>
<td class="f2">Format=</td>
<td>Certificate format</td>
</tr>
<tr>
<td class="f2">ID=</td>
<td>
Unique identifier that allows to know all files created during a given
work (associated files always have the same identifier)
</td>
</tr>
<tr>
<td class="f2">Created=</td>
<td>Creation date of the certificate</td>
</tr>
<tr>
<td class="f2">TestCount=</td>
<td>Total number of tests in the certificate</td>
</tr>
<tr>
<td class="f2">Status=</td>
<td class="last">Status of the certificate</td>
</tr>
</table>
<p></p>
<table class="details">
<tr>
<td class="f2">[Candidate]</td>
<td><b>Candidate section&nbsp;</b></td>
</tr>
<tr>
<td class="f2">File=</td>
<td>File name of the candidate</td>
</tr>
<tr>
<td class="f2">Expression=</td>
<td>Candidate expressed as a formula (if any in the input file)</td>
</tr>
<tr>
<td class="f2">N=</td>
<td>Candidate (always expressed to the base 16)</td>
</tr>
<tr>
<td class="f2">HexadecimalSize=</td>
<td>Hexadecimal size (base 16) of the candidate</td>
</tr>
<tr>
<td class="f2">DecimalSize=</td>
<td>Decimal size (base 10) of the candidate</td>
</tr>
<tr>
<td class="f2">BinarySize=</td>
<td class="last">Binary size (base 2) of the candidate</td>
</tr>
</table>
<p></p>
<table class="details">
<tr>
<td class="f2">[n]</td>
<td>
<b>Test section&nbsp;</b><br />
<br />
n is the number of the test
</td>
</tr>
<tr>
</tr>
<tr>
<td class="f2">S=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">W=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">A=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">B=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">J=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">T=</td>
<td>number expressed to the base 16</td>
</tr>
<tr>
<td class="f2">Q=</td>
<td class="last">number expressed to the base 16</td>
</tr>
</table>
<p></p>
<table class="details">
<tr>
<td class="f2">[Signature]</td>
<td><b>Signature section&nbsp;</b></td>
</tr>
<tr>
<td class="f2">1=</td>
<td>1st part of the signature of a certificate (192 bits)</td>
</tr>
<tr>
<td class="f2">2=</td>
<td class="last">2nd part of the signature of a certificate (192 bits)</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="WorkReportFile"></a></div>
<p><br /></p>
<h2>Work Report File</h2>
<div class="jtext">
After certifications or verifications, PRIMO opens the <a href="#WorkReportPage">Work
Report Page</a> and displays miscellaneous information about the work done.<br />
Work reports are automatically saved to <b>.wr</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).
</div>
<div><a name="WorkReportFileExample"></a></div>
<h3>Example of work report</h3>
<p></p>
<table class="code">
<tr>
<td>
[PRIMO - Work Report]<br />
Version=x.x.x - LX64<br />
WebSite=http://www.ellipsa.eu/<br />
Work=Certification<br />
ID=B346B00DD802B<br />
Created=???-00-0000 00:00:00 AM<br />
<br />
[Common]<br />
Path=/home/lx64/work/<br />
Selected=1<br />
Processed=1<br />
Certified=1<br />
Candidate 1=Certified, 0.03s<br />
<br />
[Candidate 1]<br />
Input=new.in<br />
Output=primo-B346B00DD802B.out<br />
Status=Candidate certified prime
</td>
</tr>
</table>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="InternalError"></a></div>
<p><br /></p>
<h2>Internal Error</h2>
<div class="jtext">
An internal error may be raised by PRIMO for mainly three reasons: a missing/corrupted file, a PRIMO bug or a
hardware failure.<br />
<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: Linux version, processor type, etc. as well as a
description of the problem (to get the current e-mail address, see the
<a href="http://www.ellipsa.eu/public/misc/contact.html">PRIMO contact page</a>).<br />
</div>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<div><a name="License"></a></div>
<p><br /></p>
<h2>License</h2>
<div class="jtext">
PRIMO - Primality Proving. Copyright &copy; 2001-2020, Marcel Martin. All rights reserved.<br />
<br />
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 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.<br />
<br />
<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.<br />
<br />
<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.<br />
<br />
<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.<br />
<br />
<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.<br />
<br />
<b>GOVERNING LAWS</b><br />
This Agreement shall be governed by the laws of France.<br />
<br />
<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 these countries.<br />
<br />
<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.<br />
<br />
<b>RESERVATION OF RIGHTS</b><br />
All rights not expressly granted in this Agreement are reserved by the Author.<br />
<br />
<i>December 8, 2020</i><br />
<i>Argenteuil, France</i>
</div>
<p class="pagefoot"><br /><a href="#Contents">Contents</a></p>
<p class="ctext">
<br />
<br />
Copyright &copy; 2020, Marcel Martin<br />
<a href="http://www.ellipsa.eu/index.html">http://www.ellipsa.eu/index.html</a><br />
</p>
</body>
</html>