[seqfan] Re: {5, 235, 72335}^2 = {25, 55225, 5232352225}

David Wilson dwilson at gambitcomm.com
Thu Dec 11 19:32:44 CET 2008

```Graziano Aglietti wrote:

OK, never mind.

I wrote a program which found the reported value then terminated. This
should have indicated that for some n, if the last n digits of n are all
prime, the last n digits of n^2 cannot all be prime.

However, I must have had an error in my program. I rewrote the program,
and now I can easily see that any n ending in 3^k 5 has n^2 ending in
2^k 5, so it is impossible to bound the length of n based on suffixes.
So my apologies there.

I rewrote the program, and for length n >= 1, I get the following
numbers of numbers k such that k has n prime digits and n^2 ends in n
prime digits:

I can tell you this:

There are no more solutions <= 26 digits.

Under reasonable assumptions about the distributions of digits, the
probability that there are any larger solutions is finite and very small.

> hello,
> could you please email the demonstration?
> thanks
> Graz
>
>
>> ==========================
>> Date: Wed, 10 Dec 2008 16:21:44 -0500
>> From: David Wilson <dwilson at gambitcomm.com>
>> To: Sequence Fanatics <seqfan at list.seqfan.eu>
>> Subject: [seqfan] Re: {5, 235, 72335}^2 = {25, 55225, 5232352225}
>> ==========================
>>
>> Yes
>>
>> zak seidov wrote:
>>
>>> Dear SeqFans,
>>>
>>> Are 5, 235, & 72335
>>>
>>> the only numbers n such that n and n^2 use only prime digits:
>>>
>>>
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>>
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```