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[ September 4, 2006 ]
Pandigital curios by Carlos Rivera (email)
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

" 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

ps. 7134562890 has the smallest largest prime factor !!

**

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

123456789
246913578 493827156 987654312 1975308624 3950617248

158729463
317458926 634917852 1269835704 2539671408 5079342816

158794623
317589246 635178492 1270356984 2540713968 5081427936

274691358
549382716 1098765432 2197530864 4395061728 8790123456

**

3) More nine- & pandigital pages

at ninedigits.htm


A000168 Prime Curios! Prime Puzzle
Wikipedia 168 Le nombre 168














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