decompwlj 3D

Primes p such that 6*p^2+1 is also prime

A153812 on the OEIS · family primes

Weight–level plate of Primes p such that 6*p^2+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 viewerA153812 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L49,163 · 49.16 %
Weight class, k ≤ L50,834 · 50.84 %
Ties, k = L6
On the level line L = 110,808
Forced level, l ≤ d²487
Range of a(n)5 … 34,372,229
Range of the jump d2 … 4,080
Largest weight k, level L34,371,917, 11,346,699

738 different gaps occur, from 2 to 4,080; the level share is 49.16 %.

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.