Primes of Form n^2 + 1

Sequence

The sequence of prime numbers of the form $n^2 + 1$ begins:

$2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, \ldots$

This sequence is A002496 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

These correspond to values of $n$ beginning:

$1, 2, 4, 6, 10, 14, 16, 20, 24, \ldots$

This sequence is A005574 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,3727 \ldots$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$