decompwlj 3D

Primes p such that 2310*p + 1 is also prime

A051653 on the OEIS · family primes

Weight–level plate of Primes p such that 2310*p + 1 is also prime
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 viewerA051653 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L34,769 · 34.77 %
Weight class, k ≤ L65,226 · 65.23 %
Ties, k = L5
On the level line L = 18,312
Forced level, l ≤ d²64
Range of a(n)2 … 6,989,273
Range of the jump d2 … 728
Largest weight k, level L6,987,751, 2,327,659

280 different gaps occur, from 2 to 728; the level share is 34.77 %.

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.