A135932 Primes whose integer square root remainder is also prime.

3, 7, 11, 19, 23, 41, 43, 47, 67, 71, 83, 103, 107, 113, 149, 151, 157, 163, 167, 199, 227, 263, 269, 331, 337, 347, 353, 419, 431, 443, 487, 491, 503, 521, 587, 593, 599, 607, 613, 617, 619, 683, 719, 787, 797, 821, 827, 907, 911, 919, 929, 937, 941, 947

Offset: 1

Author

Harry J. Smith, Dec 07 2007

Keywords

• nonn

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

• Robert Israel, Table of n, a(n) for n = 1..10000
• Wikipedia, Integer square root

Crossrefs

Cf. A053186.

Programs

Maple

filter:= proc(p) isprime(p) and isprime(p - floor(sqrt(p))^2) end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Apr 30 2025

Mathematica

f[n_]:=n-(Floor[Sqrt[n]])^2;lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)

PARI

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