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%I #20 Oct 29 2017 13:46:33
%S 47,97,197,347,547,797,1097,1447,1847,2297,2797,3347,3947,4597,5297,
%T 6047,8597,9547,11597,12697,17597,18947,20347,23297,24847,28097,31547,
%U 33347,37097,39047,41047,45197,49547,51797,61297,66347,68947,71597,74297,77047,79847
%N Primes of the form 25*n^2 + 25*n + 47.
%C The first 16 terms correspond to n from 0 to 15, which makes 25*n^2 + 25*n + 47 a prime-generating polynomial (see the link).
%C This is a prime-generating polynomial of the form s*n^2 + s*n + p, where s=k^2 and p is prime with s and p containing at most two digits. Prime-generating polynomials of this kind arise for k=1,2,3,5,7. This is the case of k=5; it generates most primes in a row out of the prime k's listed, with 12 for k=3,7, and 14 for k=2. See also A005846 and A007635 (k=1), and A048988 (k=2).
%C All terms are of the form 10m+7, with their next-to-last digits being 4 or 9.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%e 197 is a term as it is a prime corresponding to n=2: 25*4 + 25*2 + 47 = 197.
%t Select[Range[0,100]//25#^2+25#+47&, PrimeQ]
%o (PARI) for(n=0, 100, isprime(p=25*n^2+25*n+47)&& print1(p ", "))
%Y Cf. A000040 (primes), A005846, A007635, A048988, A292578 (similar prime-generating sequences).
%K nonn
%O 1,1
%A _Waldemar Puszkarz_, Oct 05 2017
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