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

1,1

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

Links

Table of n, a(n) for n=1..20.

Lucas A. Brown, A070523.py.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A138218 A056055 A359476 * A350277 A350278 A233757

Adjacent sequences: A070520 A070521 A070522 * A070524 A070525 A070526

Keyword

nonn,more

Author

Labos Elemer, May 02 2002

Extensions

More terms from Rick L. Shepherd, Jul 10 2002

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

Status

approved