A309429 Least Luhn prime in base 2n: primes p such that p + reverse(p) in base 2n is also a prime.

2, 37, 83, 137, 229, 317, 409, 557, 677, 829, 991, 1187, 1423, 1597, 1871, 2083, 2347, 2633, 2939, 3307, 3581, 3967, 4297, 4673, 5051, 5479, 5927, 6343, 6791, 7349, 7757, 8269, 8783, 9323, 9871, 10463, 11069, 11633, 12251, 12889, 13537, 14207, 14891, 15641

Offset: 1

Author

Amiram Eldar, Aug 02 2019

Keywords

• nonn
• base

Comments

Luhn primes were named after Norman Luhn, who first noted the property of 229 on the website Prime Curios!.

There are no Luhn primes in odd base, and only one, 2, in base 2.

Examples

			a(2) = 37 since 37 = 211 in base 2*2 = 4, and 211+112 = 323 which equals 59 in base 10 and is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Octavian Cira and Florentin Smarandache, Luhn prime numbers, Theory and Applications of Mathematics & Computer Science, Vol. 5, No. 1 (2015), pp. 1-8.
• G. L. Honaker, Jr. and Chris Caldwell, eds., 229, Prime Curios!, November 19, 2001.

Crossrefs

Cf. A061783.

Programs

Mathematica

a[b_] := Module[{p=2}, While[!PrimeQ[p + FromDigits[Reverse @ IntegerDigits[p, b], b]], p = NextPrime[p]]; p]; Table[a[n], {n, 2, 88, 2}]

PARI

a(n) = {my(p=2); while (!isprime(p+fromdigits(Vecrev(digits(p, 2*n)), 2*n)), p = nextprime(p+1)); p;} \\ Michel Marcus, Aug 03 2019

Formula

a(n) > 8*n^2 for n > 1.