Permutations and primes
| dc.creator | Seidov, Zakir F. | |
| dc.date | 1999-07-11 | |
| dc.date.accessioned | 2026-07-07T05:29:51Z | |
| dc.date.available | 2026-07-07T05:29:51Z | |
| dc.description | The problem of N-digit sets all permutations of which give primes is discussed. Such sets may include only digits 1, 3, 7 and 9, and none of 0, 2, 5, 4, 6, 8. Direct calculations show that such full-permutation digit sets occur at N = 1, 2, 3 and are absent in the 4 - 10 interval of N. On the other hand the formal full permutation at N = 19, 23, 317 and 1031 (as well at N = 2) cases is provided by repunits (integers all digits of which are 1). The existence/nonexistence of other (not repunits) full-permutation digit sets for arbitrary large N is an open question with probable negative answer. The maximal-permutation digit sets with maximal number of primes are given for N = 4 - 10. | |
| dc.description | 25 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/9907064 | |
| dc.identifier | http://arxiv.org/abs/math/9907064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78802 | |
| dc.subject | Number Theory | |
| dc.subject | 11M41 | |
| dc.title | Permutations and primes | |
| dc.type | text |