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A122395
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Primes of the form p^k - p^(k-1) - 1, with p prime and k>1.
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2
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3, 5, 7, 17, 19, 31, 41, 53, 109, 127, 271, 293, 499, 811, 929, 2027, 2161, 3659, 4373, 4421, 4969, 8191, 9311, 10099, 13121, 13309, 16001, 17029, 19181, 22051, 32579, 38611, 57839, 72091, 78607, 93941, 109229, 128521, 131071, 143261, 157211
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OFFSET
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1,1
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COMMENTS
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The paper by Stein and Williams gives a method for finding primes of this form when k>(p+1)/2.
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LINKS
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MAPLE
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N:= 10^6: # for terms <= N
p:= 1: R:= NULL:
do
p:= nextprime(p);
if p^2 - p - 1 > N then break fi;
for k from 2 do
q:= p^k - p^(k-1)-1;
if q > N then break fi;
if isprime(q) then R:= R, q fi;
od od:
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MATHEMATICA
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nn=10^6; lst={}; n=1; While[p=Prime[n]; k=2; While[m=p^k-p^(k-1)-1; m<nn, If[PrimeQ[m], AppendTo[lst, m]]; k++ ]; k>2, n++ ]; lst=Union[lst]
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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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