A108050 Integers k such that 10^k+21 is prime.

1, 3, 9, 17, 55, 77, 133, 195, 357, 1537, 2629, 3409, 8007, 25671, 48003, 55811, 94983, 109615, 135669

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005

Keywords

• more
• nonn

Comments

There cannot be any primes of this form when k is even, because all such numbers must be divisible by 11. A number is divisible by 11 if the difference between the sum of its odd digits and the sum of its even digits is 0 or divisible by 11. When k is even, the difference is always 0. - Dmitry Kamenetsky, Jul 12 2008

The next term, if one exists, is >100000. - Robert Price, Mar 24 2011

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10021".

Examples

			For k=3 we have 10^3+21 = 1000+21 = 1021, which is prime.
		

Links

• Makoto Kamada, List of near-repdigit-related prime numbers
• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 10^k+21, PRP Top Records.
• Index entries for primes involving repunits

Crossrefs

Cf. A049054, A088274, A088275, A138861.

Programs

Mathematica

q=21; s=""; For[ a=q,a<=q,s="10^n+"<>ToString[ a ]<>":"; n=0; For[ i=1,i< 10^3,If[ PrimeQ[ 10^i+a ],n=1; s=s<>ToString[ i ]<>"," ]; i++ ]; If[ n>0,Print[ s ] ]; a++ ] (* Vladimir Joseph Stephan Orlovsky, May 06 2008 *)

PARI

for(n=1,1e4,if(ispseudoprime(10^n+21),print1(n", "))) \\ Charles R Greathouse IV, Jul 20 2011

Extensions

a(6)=77 inserted by Vladimir Joseph Stephan Orlovsky, May 06 2008

a(13)=8007 from Dmitry Kamenetsky, Jul 12 2008

a(14)=25671 from Robert Price, Nov 08 2010

Edited by Ray Chandler, Dec 24 2010

a(15)=48003 from Robert Price, Dec 31 2010

a(16)=55811 from Robert Price, Jan 09 2011

a(17)=94983 from Robert Price, Mar 24 2011

a(18)=109615 from Lelio R Paula, added by Boyan Hu, Jul 05 2025

a(19)=135669 from Boyan Hu, Jul 05 2025