decompwlj 3D

Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime

A007510 on the OEIS · family primes · also known as Isolated (single) primes

Weight–level plate of Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is 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 viewerA007510 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L26,112 · 26.11 %
Weight class, k ≤ L73,886 · 73.89 %
Ties, k = L12
On the level line L = 18,286
Forced level, l ≤ d²14
Range of a(n)2 … 1,659,673
Range of the jump d4 … 228
Largest weight k, level L1,659,661, 331,929

Primes p with neither p - 2 nor p + 2 prime. Level share 26.11 %, a little above the primes' 23.00 %; L = 1 and L = 3 carry 60 % 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.