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A059453
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Sophie Germain primes (A005384) that are not safe primes (A005385).
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11
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2, 3, 29, 41, 53, 89, 113, 131, 173, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 743, 761, 809, 911, 953, 1013, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901
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OFFSET
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1,1
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COMMENTS
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Except for 2 and 3 these primes are congruent to 5 or 11 modulo 12.
Introducing terms of Cunningham chains of first kind.
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LINKS
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FORMULA
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EXAMPLE
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89 is a term because (89-1)/2 = 44 is not prime, but 2*89 + 1 = 179 is prime.
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MATHEMATICA
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Select[Prime[Range[300]], PrimeQ[2#+1]&&!PrimeQ[(#-1)/2]&] (* Harvey P. Dale, Nov 10 2017 *)
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PROG
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(Python)
from itertools import count, islice
from sympy import isprime, prime
def A059453_gen(): # generator of terms
return filter(lambda p:not isprime(p>>1) and isprime(p<<1|1), (prime(i) for i in count(1)))
(PARI) is(p) = isprime(p) && isprime(2*p+1) && if(p > 2, !isprime((p-1)/2), 1); \\ Amiram Eldar, Jul 15 2024
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CROSSREFS
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Cf. A005385, A053176, A059452, A059453, A059454, A059455, A007700, A005602, A023272, A023302, A023330.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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