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A247593
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Smallest prime not the middle of one 4 digits longer in base n.
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2
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OFFSET
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2,1
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COMMENTS
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a(n), n > 6, is intractable, and a(6) requires extensive resources: There are 360 candidate numbers for any candidate prime, all of which need to be composite, prefixing 30 2-digit numbers and suffixing the 12 ending in either 1 or 5. This compares with 400 for base 5, but in the base-6 case divisibility by 2 and 3 are already ruled out.
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LINKS
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EXAMPLE
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In base 2--binary, decimal 2 and 3 have representations 10 and 11; and binary 101001 and 101111 represent decimal 41 and 47, so that a(2) > 3. Binary 101--decimal 5--has the 4 binary candidates 1010101, 1010111, 1110101, and 1110111--decimal 85, 87, 117 and 119--requiring consideration for primality, but all are composite: a(2)=5.
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PROG
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(PARI) ok(n, b)=my(D=b^#digits(n, b), b2=b^2); forstep(k=b^3*D+n*b2, b2*(b2-1)*D+n*b2, D*b2, if(nextprime(k)<k+b2, return(0))); 1
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CROSSREFS
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KEYWORD
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nonn,base,more,hard
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AUTHOR
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STATUS
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approved
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