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%I #11 Jan 31 2021 22:06:42
%S 2,3,5,7,23,37,53,73,223,233,337,523,733,773,5233,33377,72733,272333,
%T 572333,5222333
%N Perfect zip primes (i.e., order-k zip primes, with k = number of digits).
%C A k-th order zip prime, where k <= number of digits, is one which, for all of each set k, form smaller primes when it is "zipped" into k parts by alternately distributing the leftmost digit to the parts. Thus 244712331139 is a 7th-order zip prime since we have:
%C k=1 244712331139
%C k=2 241313
%C ... 472319
%C k=3 2731
%C ... 4133
%C ... 4219
%C k=4 211
%C ... 421
%C ... 433
%C ... 739
%C k=5 223
%C ... 439
%C ... 43
%C ... 71
%C ... 11
%C k=6 23
%C ... 43
%C ... 41
%C ... 71
%C ... 13
%C ... 19
%C k=7 23
%C ... 41
%C ... 41
%C ... 73
%C ... 19
%C ... 2
%C ... 3
%C all primes.
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_157.htm">Zip primes</a>
%H W. Schneider, <a href="http://web.archive.org/web/2004/www.wschnei.de/digit-related-numbers/zip-primes.html">Zip Primes</a>
%K fini,full,nonn,base
%O 1,1
%A _Lekraj Beedassy_, Jul 27 2004
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