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A152127
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Sum of cousin primes < 10^n.
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2
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28, 766, 34522, 1706602, 107863996, 7379208796, 542100094312, 41248685420836, 3233516261489332, 260607555289408894, 21446383929686290726, 1795656778320649469818, 152541729206365604807782
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OFFSET
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1,1
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COMMENTS
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Cousin primes are prime pairs that differ by 4. The convention here is to count a cousin pair as long as the first cousin of the pair is less than or equal to the specified bound which in this sequence is 10^n.
"According to the first Hardy-Littlewood conjecture, the cousin primes have the same asymptotic density as the twin primes." See the MathWorld link. The (sum of cousin prime pairs < 10^n)/4 ~ number of cousin primes < 10^2n.
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LINKS
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EXAMPLE
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(3,7) and (7,11) are the cousin primes < 10. These add up to 28 the first entry in the sequence.
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PROG
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(PARI) lista(pmax) = {my(sm = 10, prev = 2, pow = 10); forprime(p = 3, pmax, if(p == prev + 4, sm += (prev + p)); if(p > pow, print1(sm, ", "); pow *= 10); prev = p); } \\ Amiram Eldar, Jul 06 2024
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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