A107291 Numbers k such that 10^k*(10^7*(-1+10^k)+6083806) + 10^k - 1 is prime.

8, 33, 41, 495, 657, 1904, 4497, 9369, 11096, 11465, 12542, 20819

Offset: 1

Author

Jason Earls, May 20 2005

Keywords

• base
• nonn
• more

Comments

These are palprimes with curved digits, i.e., palindromic primes composed of only 0's, 3s, 6s, 8s, or 9s and they have all been proved prime. No more terms up to 7000. Primality proof for the largest: PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing 10^4497*(10^7*(-1+10^4497)+6083806)+10^4497-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 5+sqrt(3) 10^4497*(10^7*(-1+10^4497)+6083806)+10^4497-1 is prime! (147.0046s+0.0074s)

Examples

			8 is a term because 10^8*(10^7*(-1+10^8)+6083806)+10^8-1 = 99999999608380699999999 is prime.
		

Links

• R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations.

Crossrefs

Cf. A079652.

Programs

PARI

is(n)=ispseudoprime(10^n*(10^7*(-1+10^n)+6083806)+10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(8)-a(12) from Michael S. Branicky, Sep 21 2024