decompwlj 3D

Emirps (primes whose reversal is a different prime)

A006567 on the OEIS · family primes · also known as Emirps

Weight–level plate of Emirps (primes whose reversal is a different 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 viewerA006567 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,988
Level class, k > L31,534 · 31.54 %
Weight class, k ≤ L68,454 · 68.46 %
Ties, k = L8
On the level line L = 17,754
Forced level, l ≤ d²20
Range of a(n)13 … 11,293,973
Range of the jump d2 … 3,000,162
Largest weight k, level L11,292,833, 3,763,549

Primes whose decimal reversal is a different prime. No emirp begins with 2, 4, 5, 6 or 8 (its reversal would be even or a multiple of 5), so whole blocks are skipped. The largest gap is 3,000,162, and 12 terms fail to decompose. The level share is 31.54 %.

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.