A070523 Numbers k such that cyclotomic(k, prime(k)) is a prime number.

3, 6, 7, 14, 19, 31, 34, 66, 93, 307, 402, 421, 600, 848, 1022, 1057, 1906, 3772, 4184, 4364

Offset: 1

Author

Labos Elemer, May 02 2002

Keywords

• nonn
• more

Comments

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

All terms <= 1906 have been proven with PARI's ECPP. No other terms <= 20000. - Lucas A. Brown, Jan 03 2021

Examples

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

Links

• Lucas A. Brown, A070523.py.

Crossrefs

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

Programs

PARI

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

Extensions

More terms from Rick L. Shepherd, Jul 10 2002

a(18)-a(20) by Lucas A. Brown, Jan 02 2021