decompwlj 3D

Primes p such that 2p-1 is also prime

A005382 on the OEIS · family primes · also known as Primes p with 2p - 1 prime

Weight–level plate of Primes p such that 2p-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 viewerA005382 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L47,756 · 47.76 %
Weight class, k ≤ L52,239 · 52.24 %
Ties, k = L27
On the level line L = 116,891
Forced level, l ≤ d²218
Range of a(n)2 … 19,347,637
Range of the jump d1 … 2,430
Largest weight k, level L19,347,607, 2,757,475

Primes p with 2p - 1 prime. The level share is 47.76 %; L = 1 holds 35 % of the level class.

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.