2657

This number is a prime.

The American mathematician Lowell Schoenfeld (1920-2002) proved that if the Riemann hypothesis was true, then

The start of a run of 14 consecutive 4-digit prime numbers separated by one-digit prime gaps. [Nie]

2657# + 1 is the smallest titanic primorial prime of form p# + 1. [Loungrides]

2657 has a peculiar property. It can be written as the sum of a power of its first digit and a power of its last digit, i.e., 2657 = 2^8 + 7^4. [Leonardis]

There are 2657 cases of a distinct-digit positive integer having a square that has exactly one odd digit. The largest has a beastly square. [Gaydos]

2657 is the 4-digit prime number p with the most primes from p to p+100. There are 19 primes from 2657 to 2757 (2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753). [Jacobs]