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[ September 4, 2006 ]
Pandigital Curios
Carlos Rivera (email)
Carlos Rivera is the webmaster of the fabulous  The prime puzzles & problems connection
1) Four ninedigitals (or zero-less pandigitals) with
the maximal quantity (8) of distinct prime factors
725638914 = 21 * 32 * 71 * 111 * 131 * 171 * 231 * 1031
789256314 = 21 * 32 * 71 * 111 * 171 * 191 * 411 * 431
856197342 = 21 * 32 * 71 * 111 * 131 * 191 * 411 * 611
961327458 = 21 * 32 * 71 * 131 * 171 * 191 * 231 * 791
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" I suppose that the same numbers ending in zero will be the champions with
9 distinct prime factors, if the same question is solved for pandigitals, but
this is not sure because there may exist some champion pandigitals with the
zero in an internal position.
I predicted just 4 solutions, yet there are 13 solutions more, all with 9
distinct prime factors. All of the 13 additional solutions are odd
not-champions in the zero-less pandigital case (7 distinct prime factors)."
Here are the solutions for pandigitals
9613274580 = 22 * 32 * 51 * 71 * 131 * 171 * 191 * 231 * 791
8961453270 = 21 * 32 * 51 * 71 * 111 * 171 * 291 * 431 * 611
8561973420 = 22 * 32 * 51 * 71 * 111 * 131 * 191 * 411 * 611
7892563140 = 22 * 32 * 51 * 71 * 111 * 171 * 191 * 411 * 431
7256389140 = 22 * 32 * 51 * 71 * 111 * 131 * 171 * 231 * 1031
7134562890 = 21 * 33 * 51 * 71 * 131 * 171 * 191 * 291 * 311
6549813270 = 21 * 32 * 51 * 71 * 111 * 131 * 231 * 291 * 1091
6542813970 = 21 * 32 * 51 * 71 * 111 * 171 * 191 * 371 * 791
5986472310 = 21 * 32 * 51 * 71 * 131 * 171 * 191 * 311 * 731
5948623170 = 21 * 32 * 51 * 71 * 171 * 191 * 231 * 311 * 411
4523786190 = 21 * 32 * 51 * 71 * 111 * 171 * 191 * 431 * 471
4386572190 = 21 * 32 * 51 * 71 * 111 * 131 * 231 * 291 * 731
3946281570 = 21 * 32 * 51 * 71 * 111 * 171 * 191 * 411 * 431
3628194570 = 21 * 32 * 51 * 71 * 111 * 131 * 171 * 231 * 1031
3561278490 = 21 * 32 * 51 * 71 * 111 * 171 * 191 * 371 * 431
3298465170 = 21 * 32 * 51 * 71 * 111 * 131 * 191 * 411 * 471
2148736590 = 21 * 32 * 51 * 71 * 111 * 131 * 171 * 231 * 611
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ps. 7134562890 has the smallest largest prime factor !!
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2) Four sequences of 6 pandigitals (of any type, zero-less or not)
such that each member (except the first one) is the double of the previous one
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3) More nine- & pandigital pages
at ninedig2.htm
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