A135933 - OEIS

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A135933

Primes whose integer square root remainder is not a prime.

2, 5, 13, 17, 29, 31, 37, 53, 59, 61, 73, 79, 89, 97, 101, 109, 127, 131, 137, 139, 173, 179, 181, 191, 193, 197, 211, 223, 229, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 307, 311, 313, 317, 349, 359, 367, 373, 379, 383, 389, 397, 401, 409, 421, 433

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OFFSET

1,1

COMMENTS

The integer square root of an integer x >= 0 can be defined as floor(sqrt(x)) and the remainder of this as x - (floor(sqrt(x)))^2.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Wikipedia, Integer square root

MATHEMATICA

Select[Prime[Range[100]], !PrimeQ[#-Floor[Sqrt[#]]^2]&] (* Harvey P. Dale, May 29 2024 *)

PROG

(PARI) { forprime(p=2, 2000, isr = sqrtint(p); Rem = p - isr*isr; if (!isprime(Rem), print1(p, ", ") ) ) }