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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