Primes whose reversal in base 10 is also prime (called "palindromic primes" by David Wells, although that name usually refers to A002385). Also called reversible primes

A007500 on the OEIS · family primes

Weight–level plate of Primes whose reversal in base 10 is also prime (called "palindromic primes" by David Wells, although that name usually refers to A002385). Also called reversible primes — 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 viewer A007500 on the OEIS

Terms	100,000 (n = 1 … 100,000)
Decomposable (a > 2d)	99,985
Level class, k > L	31,510 · 31.51 %
Weight class, k ≤ L	68,475 · 68.49 %
Ties, k = L	9
On the level line L = 1	7,753
Forced level, l ≤ d²	16
Range of a(n)	2 … 11,239,973
Range of the jump d	1 … 3,000,162
Largest weight k, level L	11,239,477, 3,746,455

255 different gaps occur, from 1 to 3,000,162; the level share is 31.51 %; 15 terms do not decompose.

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.