A070523 - OEIS

%I #32 Nov 18 2022 10:14:03

%S 3,6,7,14,19,31,34,66,93,307,402,421,600,848,1022,1057,1906,3772,4184,

%T 4364

%N Numbers k such that cyclotomic(k, prime(k)) is a prime number.

%C Values corresponding to a(3)=7 through a(13)=600 have been certified prime with Primo. Their sizes in decimal digits are 8, 10, 33, 64, 35, 51, 162, 1012, 455, 1455 and 584, respectively. Values corresponding to a(14) through a(17) are probable primes with lengths 1588, 1689, 3535 and 4014 decimal digits. a(18)>2000. - _Rick L. Shepherd_, Jul 10 2002

%C All terms <= 1906 have been proven with PARI's ECPP. No other terms <= 20000. - _Lucas A. Brown_, Jan 03 2021

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A070523.py">A070523.py</a>.

%e For n=7: 1+x+x^2+x^3+x^4+x^5+x^6 at x=prime(7)=17 gives a prime 25646167.

%o (PARI) for(n=1,2000, if(isprime(eval(polcyclo(n, prime(n)))), print1(n, ", ")))

%Y Cf. A070518, A070519, A070520, A070521, A070522.

%K nonn,more

%O 1,1

%A _Labos Elemer_, May 02 2002

%E More terms from _Rick L. Shepherd_, Jul 10 2002

%E a(18)-a(20) by _Lucas A. Brown_, Jan 02 2021