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Primes remaining primes under map 3<=>5 (interchange of decimal digits 3 and 5).
1

%I #13 Oct 30 2018 10:31:02

%S 2351,2531,3251,3257,3457,3547,3581,3659,5231,5237,5347,5381,5437,

%T 5639,13151,13159,13577,13591,13751,13757,13759,15131,15139,15377,

%U 15391,15731,15737,15739,17359,17539,23057,23357,23459,23509,23537,23549,23567,25037,25309

%N Primes remaining primes under map 3<=>5 (interchange of decimal digits 3 and 5).

%C Only primes containing at least one "3" and one "5" are considered.

%C Inspired by history (told by VIA himself) that most often mistakes made by V. I. Arnold were caused by mixing 3's and 5's (and also 2's and 9's) in the lengthy calculations by hand.

%H V. I. Arnold, <a href="http://www.mccme.ru/free-books/dubna/via-exp.pdf">Experimental observation of mathematical facts (in Russian)</a>

%e 2351,2531 both primes; 3251, 5231 both primes.

%t p = 53; Reap[Do[id = IntegerDigits[p]; If[Count[id, 3] > 0 && Count[id, 5] > 0 && PrimeQ[FromDigits[(id /. {3 -> a, 5 -> 3}) /. {a -> 5}]], Sow[p]]; p = NextPrime[p], {10^4}]][[2, 1]]

%K nonn,base

%O 1,1

%A _Zak Seidov_, Oct 20 2011