Problems & Puzzles: Conjectures

Conjecture 99. Conjecture related to A362910.

Alain Rochelli sent the following conjecture.

Strongly semiprimes p * q for which p <= q < p^3 are explained in the sequence A362910.

Let SP(A,B) the number of  strongly semiprimes between A and B and PI(A,B) the number of primes also between A and B. We conjecture that:

The ratio R(A,B) = SP(A,B) / PI(A,B) is converging to log(3) = 1.0986.. (with a sufficiently representative sample [A,B]).

For example, I computed with B-A = 2*10^6 :

A=10^9      ;   SP=104445    ;   PI=96417   ;   R=1.08326
A=10^12    ;   SP=79196     ;   PI=72413   ;    R=1.09367
A=10^18    ;   SP=52850     ;   PI=48427   ;    R=1.09133
A=10^30    ;   SP=31729     ;   PI=29054   ;    R=1.09207 

Q1. Send your own verifications.

Q2. Can you prove this conjecture?


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