decompwlj 3D

Primes of the form 6m + 1

A002476 on the OEIS · family primes · also known as Primes congruent to 1 mod 6

Weight–level plate of Primes of the form 6m + 1
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 viewerA002476 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L35,240 · 35.24 %
Weight class, k ≤ L64,758 · 64.76 %
Ties, k = L48
On the level line L = 117,936
Forced level, l ≤ d²19
Range of a(n)7 … 2,751,787
Range of the jump d6 … 270
Largest weight k, level L2,751,379, 392,815

Every term is 1 mod 6 and every gap 0 mod 6, so l = 1 (mod 6). The level share, 35.24 %, is almost the primes 5 mod 6's 35.16 %, but they have no ties and these have 48.

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.