OFFSET
0,1
COMMENTS
LINKS
H. Lifchitz and R. Lifchitz, PRP Top (275^65536+53^65536)/2.
H. Lifchitz and R. Lifchitz, PRP Top (531^131072+25^131072)/2.
Jeppe Stig Nielsen, First primes of the form (A^(2^n) + B^(2^n))/2 (gives B values).
EXAMPLE
a(10)=67 corresponds to the prime number (67^1024 + 57^1024)/2, the smallest prime number of the form (A^1024 + B^1024)/2 (or more precisely, it minimizes A).
MATHEMATICA
Table[a=1; While[Or@@PrimeQ[Table[(a^(2^n)+b^(2^n))/2, {b, a++}]]==False]; a, {n, 0, 9}] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
PROG
(PARI) for(n=0, 30, forstep(a=3, +oo, 2, forstep(b=1, a-2, 2, if(ispseudoprime((a^(2^n)+b^(2^n))/2), print1(a, ", "); next(3)))))
(Python)
from sympy import isprime
def a(n):
A, p, Ap = 3, 2**n, 3**(2**n)
while True:
if any(isprime((Ap + B**p)//2) for B in range(1, A, 2)): return A
A += 2; Ap = A**p
print([a(n) for n in range(10)]) # Michael S. Branicky, Mar 03 2021
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jeppe Stig Nielsen, Mar 26 2018
EXTENSIONS
a(16)=275 with B=53, calculated by Kellen Shenton, added by Jeppe Stig Nielsen, Nov 10 2020
a(17)=531 with B=25, by Kellen Shenton, added by Jeppe Stig Nielsen, Mar 30 2021
STATUS
approved