A258074 Table read by rows: each row represents the constant and exponent of a Colbert number.

5359, 5054502, 33661, 7031232, 28433, 7830457, 27653, 9167433, 19249, 13018586, 10223, 31172165

Offset: 1

Author

Tom Edgar, May 18 2015

Keywords

• nonn
• tabf
• fini
• more

Comments

Each row has two entries [k,n]. With this notation, the corresponding Colbert number is k*2^n+1.

A Colbert number is an integer with more than 1,000,000 digits that is prime and has contributed to the in-progress computational proof that 78557 is the smallest Sierpiński number (A076336).

a(11)-a(12) number, corresponding to [10223,31172165], is the second largest known prime that is not a Mersenne prime as of August 2023. - Hermann Stamm-Wilbrandt, Aug 13 2023

This table can only have (and is expected to have) five more rows corresponding to constants k equal to 21181, 22699, 24737, 55459, and 67607.

Examples

			The table is as follows:
  5359, 5054502;
  33661, 7031232;
  28433, 7830457;
  27653, 9167433;
  19249, 13018586
  10223, 31172165
		

Links

• C. K. Caldwell, The Prime Glossary, Colbert Number
• C. K. Caldwell, The Prime Database, 10223*2^31172165+1
• W. Sierpiński, Sur un problème concernant les nombres k * 2^n + 1, Elem. Math., 15 (1960), pp. 73-74.
• Hermann Stamm-Wilbrandt, Colbert numbers, contains entries [k,n,s,x,y] for the 6 Colbert numbers, with p=k*2^n+1, s^2%p==p-1 and p==x^2+y^2.
• Wikipedia, Seventeen or Bust

Crossrefs

Cf. A076336, A064699, A064721.

Extensions

a(11)-a(12) from Richard N. Smith, Jul 15 2019, following by the prime 10223*2^31172165+1 found by PrimeGrid.