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A093154
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Primes resulting from serial multiplication of even composites, plus 1.
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3
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5, 193, 23041, 92897281, 980995276801, 23310331287699456001, 31888533201572855808001, 13532215908553332190020108288000001, 8829205774994708066835865418197893120000001, 945837910352576904120619801361499836578686566400000001
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OFFSET
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1,1
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COMMENTS
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Primes of the form 2^n*(n+1)!+1.
a(12) = 2^118*119!+1, a(13) = 2^142*143!+1. I conjecture that a(13) is the last prime number of this form. - Jorge Coveiro, Apr 01 2004
Conjecture that a(13) is the last prime of this form is false:
a(14) = 2^2789*2780!+1 is prime
a(15) = 2^3142*3143!+1 is prime
a(16) = 2^3557*3558!+1 is prime
a(17) = 2^3686*3687!+1 is prime
a(18) = 2^4190*4191!+1 is prime
a(19) = 2^7328*7329!+1 is prime
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LINKS
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FORMULA
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Starting with 4, multiply even composites until the product plus 1 equals a prime.
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EXAMPLE
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a(1) = 5 = 2*2!+1
a(2) = 193 = 2^3*4!+1
a(3) = 23041 = 2^5*6!+1
a(4) = 92897281 = 2^8*9!+1
a(5) = 980995276801 = 2^11*12!+1
a(6) = 23310331287699456001 = 2^16*17!+1
a(11) = 2^87*88!+1 is too large to include.
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MATHEMATICA
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Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* Vincenzo Librandi, Mar 10 2015 *)
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PROG
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(Magma) [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // Vincenzo Librandi, Mar 10 2015
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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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