370 Jean-Marie De Koninck
11 968 683 934 831
the 20th powerful number n such that n + 1 is also powerful: here
11 968 683 934 831 =
132
·
793
·
3792
and 11 968 683 934 832 =
24
·
233
·
78412
(see the number 288).
13 325 427 460 800
the 21rst powerful number n such that n + 1 is also powerful: here
13 325 427, 460 800 =
26 ·33·52·72·132·1932
and 13 325 427 460 801 =
972·376332
(see the number 288).
13 346 039 198 336 (=
27
·
133
·
834)
the 100
000th
3-powerful number (see the number 216).
13 829 048 560 701
the smallest prime number which is followed by at least 700 consecutive compos-
ite numbers (in fact here by exactly 715 composite numbers); see the number
370 261.
15 061 377 048 200
the
22nd
powerful number n such that n + 1 is also powerful: here
15 061 377 048 200 =
23·52·72·1972·1992
and 15 061 377 048 201 =
36·112·732·1792
(see the number 288).
16 547 533 489 305
the largest known Wieferich number (see T. Agoh, K. Dilcher & L. Skula [2]);
we say that n is a Wieferich number if
2φ(n)
1 (mod
n2);
here is the list
of the 104 known Wieferich numbers: 1093, 3279, 3511, 7651, 10533, 14209,
17555, 22953, 31599, 42627, 45643, 52665, 68859, 94797, 99463, 127881, 136929,
157995, 228215, 298389, 410787, 473985, 684645, 895167, 1232361, 2053935,
2685501, 3697083, 3837523, 6161805, 11512569, 18485415, 19187615, 26862661,
34537707, 49887799, 57562845, 80587983, 103613121, 134313305, 149663397,
172688535, 241763949, 249438995, 310839363, 349214593, 402939915, 448990191,
518065605, 648541387, 725291847, 748316985, 1047643779, 1208819745,
1346970573, 1554196815, 1746072965, 1945624161, 2175875541, 2244950955,
3142931337, 3242706935, 3626459235, 4040911719, 4539789709, 5238218895,
5836872483, 6527626623, 6734852865, 9428794011, 9728120805, 10879377705,
Previous Page Next Page