decompwlj 3D

Primes p such that p*q+2 is prime, where q is next prime after p

A051507 on the OEIS · family primes

Weight–level plate of Primes p such that p*q+2 is prime, where q is next prime after p
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA051507 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L45,927 · 45.93 %
Weight class, k ≤ L54,069 · 54.07 %
Ties, k = L7
On the level line L = 17,934
Forced level, l ≤ d²569
Range of a(n)3 … 38,913,293
Range of the jump d2 … 5,860
Largest weight k, level L38,906,267, 12,880,699

1,330 different gaps occur, from 2 to 5,860; the level share is 45.93 %.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.