|
|
A059453
|
|
Sophie Germain primes (A005384) which are not safe primes (A005385).
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
89 is here because (89-1)/2=44 is not prime, but 2*89 + 1 = 179 is prime. Except for 2 and 3 these primes are congruent to 5 or 11 modulo 12. Introducing terms of Cunningham chains of first kind.
|
|
MATHEMATICA
|
Select[Prime[Range[300]], PrimeQ[2#+1]&&!PrimeQ[(#-1)/2]&] (* Harvey P. Dale, Nov 10 2017 *)
|
|
PROG
|
(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)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|