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%I #13 Sep 08 2022 08:45:08
%S 2,17,49877,112577,141509,1312769,3753137,5316677,6841397,9635357,
%T 31581497,33930977,37669277,41672537,45949829,47438057,62303069,
%U 84325817,93465929,130619297,149162009,162450857,172919477,191350217
%N Primes of the form 7x^3 + 5x^2 + 3x + 2.
%C More generally, we may define "primenomial primes", primes generated by polynomials of degree n with sequentially decreasing prime coefficients: Seq(m, n) = prime(n+1)x^n + prime(n)x^(n-1) + ... prime(1) for x=1..m. Here n is the degree of the polynomial, m is the range and prime(i) is the i-th prime number.
%C This is for n = 3 or 7x^3 + 5x^2 + 3x + 2.
%C Seq(m,1) gives primes of the form 3n+2: see A003627, A007528.
%C All terms except the first are == 5 mod 12. - Zak Seidov Feb 01 2009
%H Vincenzo Librandi, <a href="/A078624/b078624.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Table[7*n^3+5*n^2+3*n+2,{n,0,700}],PrimeQ] (* _Vincenzo Librandi_, Jul 15 2012 °)
%o (PARI) prnomial(n,m) = { ct=0; sr=0; p=0; d=0; d1=0; for(x=0,n, y=2; for(j=2,m+1, p = prime(j); y+=x^( j-1)*p; ); if(isprime(y),ct+=1; print1(y" "); ); ) }
%o (Magma) [a: n in [0..500] | IsPrime(a) where a is 7*n^3+5*n^2+ 3*n+2 ]; // _Vincenzo Librandi_, Jul 15 2012
%Y Cf. A003627, A007528.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Dec 11 2002, Jan 31 2009
%E Edited by _N. J. A. Sloane_, Jan 31 2009
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