A230138 List of those primes p with p + 2 and 2*p - 5 both prime.

5, 11, 17, 29, 59, 71, 101, 137, 149, 179, 197, 227, 281, 311, 431, 599, 617, 641, 809, 821, 857, 1151, 1277, 1319, 1451, 1481, 1487, 1607, 1667, 1697, 1997, 2027, 2081, 2111, 2129, 2339, 2657, 2711, 2789, 3167, 3329, 3371, 3461, 3557, 3767, 3917, 3929, 4049, 4217, 4259

Offset: 1

Author

Zhi-Wei Sun, Oct 10 2013

Keywords

• nonn

Comments

Clearly, all terms are congruent to 5 modulo 6, and not congruent to 3 modulo 5. Primes in this sequence are sparser than twin primes and Sophie Germain primes.

This sequence is interesting because of the conjectures in the comments in A230140 and A230141.

Intersection of A001359 and A089253 (or A063909). - M. F. Hasler, Oct 10 2013

Examples

			a(1) = 5 since neither 2 + 2 nor 2*3 - 5 is prime, but 5 + 2 = 7 and 2*5 - 5 = 5 are both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A005384, A230140, A230141.

Programs

Mathematica

PQ[p_]:=PQ[p]=PrimeQ[p+2]&&PrimeQ[2p-5]
m=0
Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,584}]

PARI

is_A230138(p)=isprime(p)&&isprime(p+2)&&isprime(p*2-5) \\ For large p it might be much faster to check first whether p%6==5. - M. F. Hasler, Oct 10 2013