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Numbers k such that 3^k + 5^k + 7^k + 11^k + 13^k is prime.
1

%I #22 Jun 09 2022 05:44:59

%S 0,2,4,6,12,14,28,60,68,2070,7910,10740

%N Numbers k such that 3^k + 5^k + 7^k + 11^k + 13^k is prime.

%C Note that k must be even.

%C If it exists, a(13) > 31000. - _Hugo Pfoertner_, Jun 08 2022

%e For k=2 we obtain f(2) = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373 which is a prime.

%t Select[Range[0, 1000], PrimeQ[3^# + 5^# + 7^# + 11^# +13^#] &]

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice

%o def agen(): yield from (k for k in count(0) if isprime(3**k + 5**k + 7**k + 11**k + 13**k))

%o print(list(islice(agen(), 9))) # _Michael S. Branicky_, Jun 07 2022

%Y Cf. A354831, A160773.

%K nonn,hard,more

%O 1,2

%A _Hemjyoti Nath_, Jun 07 2022

%E a(11)-a(12) from _Hugo Pfoertner_, Jun 07 2022