A069837 Smallest prime which is a concatenation of n primes.

2, 23, 223, 2237, 22273, 222323, 2222273, 22222223, 222222227, 2222222377, 22222222223, 222222223273, 2222222222273, 22222222222327, 222222222222227, 2222222222222533, 22222222222223557, 222222222222222577, 2222222222222222327, 22222222222222222253, 222222222222222222277, 2222222222222222222273, 22222222222222222222327

Offset

1,1

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400

C. Caldwell, Prime Curios!: a(101).

Mathematica

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}]

Prog

(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

Crossrefs

Cf. A036937.

Cf. A096506.

Sequence in context: A068167 A030456 A357436 * A069629 A069614 A036937

Adjacent sequences: A069834 A069835 A069836 * A069838 A069839 A069840

Keyword

base,nonn

Author

Amarnath Murthy, Apr 16 2002

Extensions

Edited, corrected and extended by Robert G. Wilson v, Apr 22 2002

Status

approved