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 Wilson the 3rd (Posted on 2012-08-07)
A prime number is called a Wilson prime
if p^2 divides (p − 1)! + 1,
There are only 3 known Wilson primes:
5, 13 and ...

Find the 3rd one.

Hint : It is a 3-digit number.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution | Comment 2 of 5 |

10   P=1
20   while P<1000
30    P=nxtprm(P)
40    Dvsr=P*P
50    Dvnd=!(P-1)+1
60    if Dvnd @ Dvsr=0 then print P,Dvsr,Dvnd
70   wend

finds

` p       p^2     (p-1)! + 1 5       25      25 13      169     479001601 563     316969          11280621026501473356049318776008263567325997858991561099487992206785121685077652349824831673837539058091447061350404912288224752676166232504987238597734405218500241472929420765736368417076000786819232752956209532030175268255198065489915076594704224416208024563555929666940501528260177644805350884559577836350020328231737458929015538184219443259901776069268002860974146270540518645360418702282857215146853858602923779882799017519412252775788781353568993148420813759218092818613683428979748535035060534255480019959564308157354162160693833915878636825625939973652741227366357593618890474378330350223278903065128884346660250635861534373558801254128426232537595947202821030418565781987924866956019256414002339142918625511039036638770053474206243724788585723410376712479127009424225586873306987931383128037254777633834757081005076422592059604736922016788198489589238019374441997355890966064057477037099668260531617003866321836270934196409597472684327571552197925036834843570347106313267355549245054957293031225081251162637010527427525120816729752007795042271699491737042324653215793950328432001647498117946267801978081671446223063712925300632803498973864795497173769781248000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001`
` `

 Posted by Charlie on 2012-08-07 16:01:19

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