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A079322
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Composite numbers of the form 1^1 * 2^2 * 3^3 * 4^4 * ... * n^n + 11.
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1
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12, 15, 119, 27659, 86400011, 4031078400011, 3319766398771200011, 55696437941726556979200011, 21577941222941856209168026828800011, 215779412229418562091680268288000000000000011
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OFFSET
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1,1
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COMMENTS
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No primes of this form in the sequence for n <= 60. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 1 for n > 3. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 11 for all n. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 61 for all n.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Volume 1, 1997, p. 116, problem 7.
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LINKS
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FORMULA
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Prod(k^k, k=1..n) + 11 is composite. Exp(log(1) + 2log(2) + 3log(3) + ... klog(k)) = exp(Sum(k*log(k), k=1..n)).
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MATHEMATICA
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Select[Table[Product[k^k, {k, n}]+11, {n, 10}], CompositeQ] (* Harvey P. Dale, Jun 12 2016 *)
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PROG
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(PARI) pcomposits(n, b) = { for(x=1, n, p=1; for(y=1, x, p = p*(y^y); ); if(!isprime(p+b), print1(p+b", ")); ) }
(Python)
from sympy import isprime
from itertools import count
def agen():
p = 1
for k in count(1):
p *= k**k
if not isprime(p + 11):
yield p + 11
g = agen()
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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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STATUS
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approved
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