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 Nth prime.
There is only one other such 10 digit number: can you find it?
I did this by hand calculator only (1 hour elapsed time) and found every number of every length.
There are four one digit numbers that work where we might expect 9/2 = 4.5
There are 13 two digit numbers. Expected 99/(2*3) = 16.5
26 three digit and 999/(2*3*5) = 33.3
43 four digit and 9999/(2*3*5*7) = 47.61
39 five digit and (10^5  1)/(2*3*5*7*9) = 43.29
33 six digit expect 33.3
23 seven digit expect 19.59
10 eight digit expect 10.31
4 nine digit expect 4.48
2 ten digit expect 1.55
0 eleven digit expect .4986

Posted by Jer
on 20050104 18:20:26 