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A108050
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Integers n such that 10^n+21 is prime.
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27
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1, 3, 9, 17, 55, 77, 133, 195, 357, 1537, 2629, 3409, 8007, 25671, 48003, 55811, 94983
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| There cannot be any primes of this form when n 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 n is even the difference is always 0. - Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jul 12 2008
The next term, if one exists, is >100000. [From Robert Price (pamandbobprice(AT)yahoo.com), 24 March 2011]
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable/proven prime - search on "10021".
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LINKS
| Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.
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EXAMPLE
| For n=3 we have 10^3+21 = 1000+21 = 1021, which is prime.
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MATHEMATICA
| 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 Orlovsky, May 06 2008
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PROG
| (PARI) for(n=1, 1e4, if(ispseudoprime(10^n+21), print1(n", "))) \\ Charles R Greathouse IV, Jul 20 2011
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CROSSREFS
| Cf. A049054, A088274, A088275.
Sequence in context: A176354 A173140 A018307 * A009211 A105538 A056404
Adjacent sequences: A108047 A108048 A108049 * A108051 A108052 A108053
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KEYWORD
| more,nonn
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AUTHOR
| Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005
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EXTENSIONS
| Insert a(6)=77 by Vladimir Orlovsky, May 06 2008
a(13)=8007 from Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jul 12 2008
a(14)=25671 from Robert Price (pamandbobprice(AT)yahoo.com), Nov 08 2010
Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 24 2010
a(15)=48003 from Robert Price (pamandbobprice(AT)yahoo.com), Dec 31 2010
a(16)=55811 from Robert Price (pamandbobprice(AT)yahoo.com), Jan 09 2011
a(17)=94983 from Robert Price (pamandbobprice(AT)yahoo.com), Mar 24 2011
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