A133957 Form the list of home primes A037274(c) for c composite, and sort into increasing order.

23, 37, 211, 223, 227, 229, 233, 241, 257, 271, 277, 283, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 523, 541, 547, 557, 571, 577, 719, 743, 761, 773, 797, 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747

Offset: 1

Author

Robert G. Wilson v, Sep 30 2007

Keywords

• nonn
• base

Comments

The old name was "Home primes the result of composite numbers."

Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....

Increasing sequence of all prime numbers which are concatenations of at least two primes ordered in nondecreasing order (e.g., 227=2.2.7, 1319=13.19). - Bartlomiej Pawlik, Aug 06 2023

Examples

			The home primes corresponding to the first few composite numbers c are as follows:
   c            A037274(c)
   4            211
   6            23
   8            3331113965338635107
   9            311
   10           773
   12           223
   14           13367
   15           1129
   16           31636373
   18           233
   20           3318308475676071413
   21           37
   ...          ...
		

Links

• Patrick De Geest, Home Primes < 100 and Beyond.
• Eric Weisstein's World of Mathematics, Home Prime.

Crossrefs

Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

Mathematica

lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}]; Union@ lst

Extensions

Entry revised by N. J. A. Sloane, Mar 24 2021