A307176 Number of Sophie Germain primes of the form 4k + 1 less than 10^n.

1, 5, 17, 89, 589, 3833, 27940, 211439, 1653257, 13283194, 109058142, 911411528, 7731354496

Offset: 1

Author

Rodolfo Ruiz-Huidobro, Mar 27 2019

Keywords

• nonn
• more

Comments

Sophie Germain primes can alternatively be Lucasian primes, primes of the form 4k + 1, or, the individual prime 2.

Examples

			There are five Sophie Germain Primes of the form 4k + 1 below 10^2: {5, 29, 41, 53, 89}, therefore a(2) = 5.
		

Crossrefs

Cf. A091098, A092816, A002515, A307121, A002144, A005384, A103579.

Programs

Mathematica

nonLucSophies = Select[4Range[2500000] + 1, PrimeQ[#] && PrimeQ[2# + 1] &]; Table[Length[Select[nonLucSophies, # < 10^n &]], {n, 0, 7}]

Formula

a(n) < A092816(n).

a(n) <= A091098(n) (with equality for n = 1).

a(n) = A092816(n) - A307121(n) - 1.