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A215725
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Numbers x such that 2*x+1 is prime as is 2*x+3 and x^2+x+41 and (x+1)^2+(x+1)+41.
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1
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1, 2, 5, 8, 14, 20, 29, 35, 50, 53, 68, 74, 98, 113, 119, 134, 230, 404, 413, 509, 575, 650, 713, 725, 809, 893, 935, 938, 974, 1013, 1043, 1133, 1190, 1400, 1625, 1730, 1778, 1958, 2045, 2318, 2510, 2933, 2939, 3224, 3344, 3389, 3743, 3773
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OFFSET
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1,2
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COMMENTS
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p=x^2+x+41 and q = (x+1)^2+(x+1)+41, (x+p)^2+x+p+41 = p*q is a semiprime.
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LINKS
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EXAMPLE
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1^2+1+41=43=p , 2^2+2+41=47=q , (43+1)^2+(43+1)+41=p*q.
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MATHEMATICA
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Select[Range[4000], And@@PrimeQ[{2#+1, 2#+3, #^2+#+41, (#+1)^2+#+42}]&] (* Harvey P. Dale, Jun 02 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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