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A136721
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Prime quadruples: 3rd term.
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2
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11, 17, 107, 197, 827, 1487, 1877, 2087, 3257, 3467, 5657, 9437, 13007, 15647, 15737, 16067, 18047, 18917, 19427, 21017, 22277, 25307, 31727, 34847, 43787, 51347, 55337, 62987, 67217, 69497, 72227, 77267, 79697, 81047, 82727, 88817, 97847
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OFFSET
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1,1
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COMMENTS
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Primes p such that p-6, p-4, and p+2 are prime. Apart from the first term, a(n) = 17 (mod 30).
The members of each quadruple are twin primes when they are 1st and 2nd terms and when 3rd and 4th terms. When they are 2nd and 3rd terms they differ by 4.
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LINKS
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FORMULA
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EXAMPLE
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The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.
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MAPLE
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p2:= 0: p3:= 0: p4:= 0:
Res:= NULL: count:= 0:
while count < 100 do
p1:= p2; p2:= p3; p3:= p4;
p4:= nextprime(p4);
if [p2-p1, p3-p2, p4-p3] = [2, 4, 2] then
count:= count+1; Res:= Res, p3
fi
od:
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MATHEMATICA
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lst={}; Do[p0=Prime[n]; If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p6]]]], {n, 12^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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