decompwlj 3D

Primes of form 10n+3

A030431 on the OEIS · family primes · also known as Primes ending in 3

Weight–level plate of Primes of form 10n+3
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 viewerA030431 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L37,279 · 37.28 %
Weight class, k ≤ L62,718 · 62.72 %
Ties, k = L0
On the level line L = 19,631
Forced level, l ≤ d²60
Range of a(n)3 … 5,796,823
Range of the jump d10 … 540
Largest weight k, level L5,795,753, 526,953

Primes ending in 3. Every gap is a multiple of 10, so l ends in 3; no square ends in 3, so there are no ties, by proof. The level share is 37.28 %.

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.