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A258074
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Table read by rows: each row represents the constant and exponent of a Colbert number.
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0
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5359, 5054502, 33661, 7031232, 28433, 7830457, 27653, 9167433, 19249, 13018586, 10223, 31172165
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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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.
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EXAMPLE
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The table is as follows:
5359, 5054502;
33661, 7031232;
28433, 7830457;
27653, 9167433;
19249, 13018586
10223, 31172165
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CROSSREFS
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KEYWORD
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nonn,tabf,fini,more
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AUTHOR
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EXTENSIONS
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a(11)-a(12) from Richard N. Smith, Jul 15 2019, following by the prime 10223*2^31172165+1 found by PrimeGrid.
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STATUS
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approved
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