A304390 Prime numbers p such that p squared + (p reversed) squared is also prime.

23, 41, 227, 233, 283, 401, 409, 419, 421, 461, 491, 499, 823, 827, 857, 877, 2003, 2083, 2267, 2437, 2557, 2593, 2617, 2633, 2677, 2857, 2887, 2957, 4001, 4021, 4051, 4079, 4129, 4211, 4231, 4391, 4409, 4451, 4481, 4519, 4591, 4621, 4639, 4651, 4871, 6091, 6301, 6329, 6379, 6521, 6529, 6551

Offset: 1

Author

Pierandrea Formusa, Aug 16 2018

Keywords

• nonn
• base

Examples

			The prime number 227 belongs to this sequence as 722 is 227 reversed and 227^2 + 722^2 = 572813, which is prime.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A061783 (Luhn primes).

Subsequence of A069207. - Michel Marcus, Aug 21 2018

Programs

Mathematica

Select[Prime@ Range@ 850, PrimeQ[#^2 + FromDigits[ Reverse@ IntegerDigits@ #]^2] &] (* Giovanni Resta, Sep 03 2018 *)

PARI

isok(p) = isprime(p) && isprime(p^2+eval(fromdigits(Vecrev(digits(p))))^2); \\ Michel Marcus, Aug 21 2018

Python

nmax=10000
def is_prime(num):
    if num == 0 or num == 1: return(0)
    for k in range(2, num):
       if (num % k) == 0:
           return(0)
    return(1)
ris = ""
for i in range(nmax):
    r=int((str(i)[::-1]))
    t=pow(i,2)+pow(r,2)
    if is_prime(i):
       if is_prime(t):
          ris = ris+str(i)+","
print(ris)