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Prime divisors (Posted on 2005-01-04) Difficulty: 3 of 5
6300846559 is such that 6 is divisible by 2; 63, by 3; 630, by 5; 6300, by 7; and, in general, if you take its first N digits, it will be divisible by the N-th prime.

There is only one other such 10 digit number: can you find it?

See The Solution Submitted by e.g.    
Rating: 3.7500 (4 votes)

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re: A further analysis | Comment 7 of 11 |
(In reply to A further analysis by Jer)

The program had found 44 (rather than 43) that are four digits:

2100, 2107, 2156, 2401, 2408, 2450, 2457, 2702, 2709, 2751, 2758, 4200, 4207, 4256, 4501, 4508, 4550, 4557, 4802, 4809, 4851, 4858, 6006, 6055, 6300, 6307, 6356, 6601, 6608, 6650, 6657, 6902, 6909, 6951, 6958, 8106, 8155, 8400, 8407, 8456, 8701, 8708, 8750, 8757

It found 24 (rather than 23) that were seven digits:

2107694, 2156059, 2401369, 2450890, 2751195, 2758862, 4200955, 4207585, 4508927, 4550781, 4851086, 4858753, 6055536, 6300846, 6307476, 6608818, 6650672, 6958644, 8155427, 8400737, 8407367, 8708709, 8750563, 8757193

and 11 (rather than 10) that were eight digits:

21076947, 21560592, 27588627, 42009551, 45507812, 63008465, 66506726, 81554270, 84007379, 84073670, 87571931

 


  Posted by Charlie on 2005-01-04 18:51:16
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