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A061783
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Luhn primes: primes p such that p + (p reversed) is also a prime.
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13
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229, 239, 241, 257, 269, 271, 277, 281, 439, 443, 463, 467, 479, 499, 613, 641, 653, 661, 673, 677, 683, 691, 811, 823, 839, 863, 881, 20011, 20029, 20047, 20051, 20101, 20161, 20201, 20249, 20269, 20347, 20389, 20399, 20441, 20477, 20479, 20507
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OFFSET
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1,1
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COMMENTS
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a(n) has an odd number of digits, as otherwise a(n) + reverse(a(n)) is a multiple of 11. For a(n) > 10, a(n) is prime and thus odd, and therefore the first digit of a(n) is even as otherwise a(n) + reverse(a(n)) is even and composite. - Chai Wah Wu, Aug 19 2015
Named by Cira and Smarandache (2014) after Norman Luhn who noted the property of the prime 229 on the Prime Curios! website. - Amiram Eldar, Jun 05 2021
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LINKS
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Octavian Cira and Florian Smarandache, Luhn prime numbers, Theory and Applications of Mathematics & Computer Science, Vol. 5, No. 1 (2015), pp. 29-36; preprint, 2014.
G. L. Honaker, Jr. and Chris Caldwell, eds., 229, Prime Curios!, November 19, 2001.
Chai Wah Wu, 3010506 terms, 11MB zipped file of all terms below 10^9.
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EXAMPLE
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229 is a term since 229 is a prime and so is 229 + 922 = 1151.
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MATHEMATICA
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Select[Prime[Range[3000]], PrimeQ[#+FromDigits[Reverse[IntegerDigits[#]]]]&] (* Harvey P. Dale, Nov 27 2010 *)
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PROG
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(PARI) { n=0; forprime (p=2, 86843, x=p; r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); if (isprime(p + r), write("b061783.txt", n++, " ", p)) ) } \\ Harry J. Smith, Jul 28 2009
(PARI) select( is_A061783(p)=isprime(A056964(p)) && isprime(p), primes(8713)) \\ A056964(p)=p+fromdigits(Vecrev(digits(p))). There is no term with 4 digits or starting with an odd digit, i.e., no candidate between prime(168) = 997 and prime(2263) = 20011. Using primes up to prime(8713) = 89989 ensures the list of 5-digit terms is complete. - M. F. Hasler, Sep 26 2019
(Magma) [NthPrime(n): n in [1..2400] | IsPrime(s) where s is NthPrime(n)+Seqint(Reverse(Intseq(NthPrime(n))))]; // Bruno Berselli, Aug 05 2013
(Python)
from sympy import isprime, prime
A061783 = [prime(n) for n in range(1, 10**5) if isprime(prime(n)+int(str(prime(n))[::-1]))] # Chai Wah Wu, Aug 14 2014
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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