| Displaying 1-3 of 3 results found.
page
1
Concatenation of prime p and nextprime(p) is prime -> cycles of 2 steps possible.
+10
3
467, 941, 13681, 14461, 21787, 22171, 22369, 24049, 24151, 25457, 29333, 37397, 41221, 42467, 43481, 46511, 48023, 54133, 56681, 68699, 75883, 85081, 101341, 103511, 117443, 120193, 126199, 137363, 144323, 145133, 158791, 175853, 181891, 183797
EXTENSIONS
Offset corrected and missing 181891 inserted by Sean A. Irvine, Oct 26 2020
Concatenation of prime p and nextprime(p) is prime -> cycles of 3 steps possible.
+10
3
467, 941, 959941, 3396199, 4858943, 5696101, 6475643, 7566133, 7584253, 7592261, 9305281, 9463877, 11430491, 13442243, 14374837, 15941473, 17414497, 17691997, 19584223, 21421849, 22310159, 22808459, 27601163, 29198881
COMMENTS
Terms from 3396199 up to 17691997 found by Jo Yeong Uk (hyukjo(AT)sigma.chungnam.ac.kr).
Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.
+10
0
3, 2, 13681, 467, 127787377, 200603842261
EXAMPLE
Let "|" denote concatenation.
3 | 5 = 35, which is not prime, so a(0) = 3.
2 | 3 = 23 (prime), 23 | 29 = 2329 (composite), so a(1) = 2.
13681 | 13687 (prime), 1368113687 | 1368113699 (prime), 13681136871368113699 | 13681136871368113711 (composite), so a(2) = 13681.
MATHEMATICA
a[n_] := Block[{pp=1, p, q, c=-1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]
Search completed in 0.004 seconds
| 