A075705 Safe primes (A005385) (p and (p-1)/2 are primes) such that 6*p+1 is also prime.
5, 7, 11, 23, 47, 83, 107, 263, 347, 467, 503, 863, 887, 1283, 1487, 1823, 1907, 2027, 2063, 2447, 2903, 3203, 3623, 4007, 4127, 4547, 4703, 4787, 5387, 5807, 7523, 7703, 8147, 8423, 11423, 11483, 11807, 12107, 12227, 12647, 12983, 13043, 13163, 14087, 14207
Offset: 1
Keywords
Examples
47 is prime, so is (47-1)/2=23 and also 6*47+1=283; 83 is a prime, (83-1)/2=41 and 6*83+1=499, ...
Links
- David Consiglio, Jr. and T. D. Noe, Table of n, a(n) for n = 1..1000
Programs
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Maple
ts_sg_var_pras := proc(nmax) local i,tren,atek; tren := 0: for i from 1 to nmax do atek := numtheory[safeprime](i): if (atek > tren) then if (isprime(atek)='true' and isprime(6*atek+1)='true') then tren := atek: fi; fi; od; end: seq(ts_sg_var_pras(i), i=1..3000);
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Mathematica
Select[Range[20000], PrimeQ[#] && PrimeQ[(#-1)/2] && PrimeQ[6#+1] &] (* T. D. Noe, Nov 07 2011 *) Select[Prime[Range[1700]],And@@PrimeQ[{(#-1)/2,6#+1}]&] (* Harvey P. Dale, Feb 28 2013 *)