Hello MathFun, none of those integers are prime numbers. Will we find such a "pendulum prime" soon? 1 21 213 4213 42135 642135 6421357 86421357 864213579 10864213579 1086421357911 121086421357911 12108642135791113 1412108642135791113 141210864213579111315 16141210864213579111315 1614121086421357911131517 181614121086421357911131517 18161412108642135791113151719 ... This sequence can be found in the OEIS: https://oeis.org/A053063 Note that this one claims that « a(n) is not prime for any n <= 3000 »: https://oeis.org/A281254 Best, Merry Xmas, É. P.-S. The opening picture (invisible in this mail but visible on my personal blog) is by Kay Rosen: https://bit.ly/2s11v90