A248046 Primes p such that p^2 is the concatenation of two k-digit primes where k is half the length of p^2.
5, 73, 337, 409, 701, 827, 5449, 5477, 5939, 6841, 7417, 8353, 8573, 9109, 9227, 9311, 9733, 9767, 32569, 34319, 34327, 34501, 35933, 35999, 38371, 38449, 38923, 38953, 39023, 39367, 39671, 40531, 40973, 42701, 43543, 44651, 45259, 46021, 47623, 48311, 49531, 50923, 54133, 54437, 54547
Offset: 1
Examples
73 is prime, and 73^2 = 5329 is the concatenation of two 2-digit primes (53 and 29). So 73 is a member of this sequence. 929 is not in the sequence since 929^2 = 863041, where 863 is a 3-digit prime but 041 is a 2-digit prime. - _Jens Kruse Andersen_, Oct 06 2014
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
Programs
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PARI
forprime(p=1,10^5,d=digits(p^2);if((#d)%2==0,if(isprime((p^2)\(10^(#d/2)))&&isprime((p^2)%(10^(#d/2)))&&#Str((p^2)%(10^(#d/2)))==#d/2,print1(p,", "))))
Extensions
Terms and program corrected by Derek Orr to match definition, thanks to Jens Kruse Andersen