Prime Gaps of 10

Theorem

The following pairs of consecutive prime numbers are those whose difference is 10$10$:

(139,149),(181,191),(241,251),(283,293),…$(139,149),(181,191),(241,251),(283,293),\dots$

The sequence of the lower elements is A031928 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Demonstrated by listing the prime gaps.

■$◼$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): 139$139$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): 139$139$