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One and only (Posted on 2016-04-28)

There is only one prime p such that p! is p digits long.

Find it and prove its uniqueness.

See The Solution Submitted by Ady TZIDON

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25!=15511210043330985984000000 which is 25 digits long.

p! = p*(p-1)!. Then for p>=10, p! has at least one more digit than (p-1)!.

For p<25, only 23 works: 23! = 25852016738884976640000.

Posted by xdog on 2016-04-28 09:52:53

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