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A108050
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Integers k such that 10^k+21 is prime.
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28
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1, 3, 9, 17, 55, 77, 133, 195, 357, 1537, 2629, 3409, 8007, 25671, 48003, 55811, 94983
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OFFSET
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1,2
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COMMENTS
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There cannot be any primes of this form when k is even, because all such numbers must be divisible by 11. A number is divisible by 11 if the difference between the sum of its odd digits and the sum of its even digits is 0 or divisible by 11. When k is even, the difference is always 0. - Dmitry Kamenetsky, Jul 12 2008
The next term, if one exists, is >100000. - Robert Price, Mar 24 2011
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10021".
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LINKS
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EXAMPLE
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For k=3 we have 10^3+21 = 1000+21 = 1021, which is prime.
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MATHEMATICA
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q=21; s=""; For[ a=q, a<=q, s="10^n+"<>ToString[ a ]<>":"; n=0; For[ i=1, i< 10^3, If[ PrimeQ[ 10^i+a ], n=1; s=s<>ToString[ i ]<>", " ]; i++ ]; If[ n>0, Print[ s ] ]; a++ ] (* Vladimir Joseph Stephan Orlovsky, May 06 2008 *)
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PROG
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005
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EXTENSIONS
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STATUS
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approved
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