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A100596
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Numbers k such that (prime(k)-1)! + prime(k)^10 is prime.
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1
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OFFSET
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1,1
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COMMENTS
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k = {2, 8, 15, 33, 52, 205} yields primes p(k) = {3, 19, 47, 137, 239, 1259}. There are no more such k up to k=150. Computed in collaboration with Ray Chandler.
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LINKS
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FORMULA
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Primes of the form (prime(k)-1)! + prime(k)^10, where prime(k) is the k-th prime.
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EXAMPLE
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a(1) = 2 because (prime(2)-1)! + prime(2)^10 = (3-1)! + 3^10 = 59051 is the smallest prime of that form.
a(2) = 8 because (prime(8)-1)! + prime(8)^10 = (19-1)! + 19^10 = 6408504771985801 is the 2nd smallest prime of that form.
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MATHEMATICA
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PROG
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(Python)
from math import factorial
from sympy import isprime, prime
def afind(limit, startat=1):
for k in range(startat, limit+1):
s = str(k)
pk = prime(k)
if isprime( factorial(pk-1) + pk**10 ):
print(k, end=", ")
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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