Prime Gaps of 10

Theorem

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

$\tuple {139, 149}, \tuple {181, 191}, \tuple {241, 251}, \tuple {283, 293}, \ldots$

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.

$\blacksquare$

Sources

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