A198047 -id:A198047 - cp's OEIS frontend

A198146 Primes remaining primes under map 2<=>9 (interchange of decimal digits 2 and 9).

2293, 2393, 2591, 2693, 2791, 2903, 2957, 5297, 5927, 7297, 7927, 8293, 8923, 9203, 9257, 9323, 9521, 9623, 9721, 9923, 12491, 12497, 12907, 12911, 12967, 12973, 13291, 13921, 14293, 14923, 17291, 17293, 17921, 17923, 19207, 19211, 19267, 19273, 19421, 19427

Offset: 1

Zak Seidov, Oct 21 2011

Only primes containing at least one "2" and one "9" are considered.

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

			2293, 9923 both primes; 2393, 9323 both primes.

V. I. Arnold, Experimental observation of mathematical facts (in Russian)

Cf. A198047 (map 3 <=> 5).

p = 29; Reap[Do[id = IntegerDigits[p]; If[Count[id, 2] > 0 && Count[id, 9] > 0 && PrimeQ[FromDigits[(id /. {2 -> a, 9 -> 2}) /. {a -> 9}]], Sow[p]]; p = NextPrime[p], {10^4}]][[2,1]]

A386528 Primes which remain primes after the mapping {1 -> 3, 3 -> 5, 5 -> 7, 7 -> 9, 9 -> 1} of its decimal digits.

Original entry on oeis.org

2, 3, 5, 19, 31, 37, 41, 59, 97, 131, 137, 151, 157, 181, 191, 199, 211, 227, 239, 271, 281, 307, 349, 359, 367, 409, 419, 457, 461, 479, 509, 541, 569, 619, 631, 641, 691, 727, 797, 821, 827, 829, 881, 907, 919, 947, 971, 977, 991, 1009, 1021, 1049, 1069, 1087, 1097, 1109, 1151

Offset: 1

Tristan J. Jones and Robert G. Wilson v, Aug 21 2025

Of the 10! possible nontrivial decimal digital mappings, this one was chosen for its inclusion of all the odd numbers and none of the even numbers.

			19 is a term since the mapping produces 31, which is prime;
31 is a term since the mapping produces 53, which is prime.

Cf. A000040, A198047.

fQ[n_] := PrimeQ[ FromDigits[ IntegerDigits[ n] /. {1 -> 3, 3 -> 5, 5 -> 7, 7 -> 9, 9 -> 1}]]; Select[ Prime@ Range@ 200, fQ]

from sympy import isprime
def ok(n): return isprime(n) and isprime(int(str(n).translate(str.maketrans("13579","35791"))))
print([k for k in range(1200) if ok(k)]) # Michael S. Branicky, Aug 24 2025

cp's OEIS Frontend

A198146 Primes remaining primes under map 2<=>9 (interchange of decimal digits 2 and 9).

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