378 Jean-Marie De Koninck
t n
1 18 (one can prove that it is the only solution)
2 12, 24, 35, 56
3 (no known solution)
4 120, 315, 4 752, 7 744, 24 960, 57 915, 3 386 880
5 50, 210, 450, 780, 1 500, 3 920, 16 500, 91 728, 269 500, 493 920,
1 293 600, 266 378 112, 317 447 424, 1 277 337 600,
14 948 388 000, 48 697 248 600, 379 748 636 467 200
6 90, 840, 4 320, 59 400, 60 480, 917 280, 2 419 200,
34 992 000, 3 714 984 000, 460 522 782 720,
896 168 448 000, 2 194 698 240 000, 39 109 522 636 800,
229 419 122 688 000, 239 446 056 960 000, 650 997 662 515 200,
3 954 407 288 832 000, 182 279 345 504 256 000,
883 270 791 696 384 000
7 8 314 460 009 856 000, 31 746 120 037 632 000,
92 632 873 013 093 597 184 000 000,
1 108 240 107 492 643 314 063 114 240 000
8 (no known solution)
9 (no known solution)
9 077 457 159 999 998
possibly the second number n such that min(λ(n), λ(n + 1), λ(n + 2)) 1.7;
here we have
min(λ(n), λ(n + 1), λ(n + 2)) min(1.83944, 1.73736, 1.70566) = 1.70566;
see the number 85 016 574 for the smallest number n satisfying the above in-
equality.
9 999 999 999 999 937
the largest 16 digit prime number.
10 000 000 000 000 061
the smallest 17 digit prime number.
11 111 731 111 111 113
the smallest odd insolite number whose digits are not only 1’s; the smallest five
numbers satisfying this
property211
are 11 111 731 111 111 113,
11 117 311 111 311 111, 11 131 117 111 113 111, 13 111 131 117 111 111 and
17 111 113 131 111 111.
211One
can prove that, except for these five numbers, any other number satisfying this property is
larger than 1021.
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