near-square prime


A near-square primeMathworldPlanetmath is a prime numberMathworldPlanetmath p of the form n2+k, with n being any integer and 0<|k|<|n| also an integer. Since for any nonzero real number x it is always the case that x20, it doesn’t matter if n is negative.

5 149
4 29 53
3 67 103
2 11 83
1 5 17 37 101
0 1 4 9 16 25 36 49 64 81 100 121 144
-1 3
-2 7 23 47 79
-3 97
-4
-5 31 59 139

Fermat primesMathworldPlanetmath are near-square primes for k=1 with the additional requirement that n=22m-1, while Carol primes are near-square primes for k=-2 with the additional requirement that n=2m-1.

For k=-1, only n=2 gives a prime, namely 3.

Title near-square prime
Canonical name NearsquarePrime
Date of creation 2013-03-22 18:57:37
Last modified on 2013-03-22 18:57:37
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41