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A069837
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Smallest prime which is a concatenation of n primes.
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4
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2, 23, 223, 2237, 22273, 222323, 2222273, 22222223, 222222227, 2222222377, 22222222223, 222222223273, 2222222222273, 22222222222327, 222222222222227, 2222222222222533, 22222222222223557, 222222222222222577, 2222222222222222327, 22222222222222222253, 222222222222222222277, 2222222222222222222273, 22222222222222222222327
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OFFSET
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1,1
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COMMENTS
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Conjecture: For every n there exists an n-digit prime which is composed of the digits 2,3,5 and 7. I.e., no prime > 7 is required in this concatenation. I.e., a(n) of A069637 contains exactly n digits. This is a weaker conjecture than the one by Patrick De Geest in A036937.
If the conjecture is true then this also gives the smallest n-digit prime with prime digits. - Amarnath Murthy, Apr 02 2003
Except for the first term, A096506 lists indices n=2,3,8,11,36,95,101,128,... for which a(n) is of the form 2...23. - M. F. Hasler, Apr 25 2008
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LINKS
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MATHEMATICA
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f[n_] := Block[{p = 2(10^n - 1)/9}, While[ !PrimeQ[p] || Union[ PrimeQ[ IntegerDigits[p]]] != {True}, p++ ]; p]; Table[ f[n], {n, 1, 20}]
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PROG
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(PARI) A069837(n)={ local( p=(10^n-1)\9*2-1 ); n=Vec("2357"); until( !setminus( Set(Vec(Str(p))), n), p=nextprime(p+1)); p } /* a more efficient version should check digits one by one and skip to the next possible candidate (i.e., add 12...23 - p%10^d) when a nonprime digit is found */ \\ M. F. Hasler, Apr 25 2008
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CROSSREFS
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KEYWORD
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base,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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