A107291 - OEIS

%I #18 Sep 22 2024 02:06:53

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

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

%C 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)

%H R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/">The Top Ten: a Catalogue of Primal Configurations</a>.

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

%o (PARI) is(n)=ispseudoprime(10^n*(10^7*(-1+10^n)+6083806)+10^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A079652.

%K base,nonn,more

%O 1,1

%A _Jason Earls_, May 20 2005

%E a(8)-a(12) from _Michael S. Branicky_, Sep 21 2024