

A242708


Primes p such that p^2 + p + 41 is semiprime.


1



41, 89, 109, 127, 163, 173, 239, 251, 271, 283, 331, 347, 349, 367, 373, 383, 389, 401, 409, 421, 443, 449, 463, 467, 487, 547, 557, 563, 569, 571, 577, 587, 593, 613, 643, 661, 701, 727, 733, 739, 761, 769, 773, 797, 823, 827, 853, 857, 881, 907, 937, 947, 971
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OFFSET

1,1


COMMENTS

n^2+n+41 is sometimes referred to as Euler's polynomial.
A242702 is for semiprimes such that n^2+n+41 is also semiprime.


LINKS



EXAMPLE

41 is prime and 41^2 + 41 + 41 = 1763 = 41 * 43 is semiprime. Hence, 41 is in the sequence.
127 is prime and 127^2 + 127 + 41 = 16297 = 43 * 379 is semiprime. Hence, 127 is in the sequence.
43 is prime and 43^2 + 43 + 41 = 1933 which is prime (not semiprime). Hence, 43 is not in the sequence.


MAPLE

with(numtheory): A242708:= proc(); if isprime(n) and bigomega(n^2+n+41)=2 then RETURN (n); fi; end: seq(A242708 (), n=1..1000);


MATHEMATICA

c = 0; Do[If[PrimeQ[n] && PrimeOmega[n^2 + n + 41] == 2, c++; Print[c, " ", n]], {n, 1, 3*10^5}];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



