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 Primed and Perfect (Posted on 2014-01-03)
Determine the minimum value of a positive integer n > 1 such that n + 6 is a prime number and 9*n + 7 is a perfect square.

What are the next two smallest values of n with this property?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 1 of 1

10   for N=1 to 999999
20     P=N+6
30     if prmdiv(P)=P then
40          :Sq=9*N+7
50          :Sr=int(sqrt(Sq)+0.5)
60          :if Sr*Sr=Sq then print N,P,Sq,Sr
70             :Ct=Ct+1:if Ct>45 then stop
80   next

finds the first three values of n higher than 1 are 53, 277 and 373:

`  n             n + 6           9*n + 7      sqrt(9*n+7)1               7               16              453              59              484             22277             283             2500            50373             379             3364            58641             647             5776            76821             827             7396            861393            1399            12544           1123061            3067            27556           1663761            3767            33856           1844993            4999            44944           2126293            6299            56644           2387861            7867            70756           2669473            9479            85264           29210133           10139           91204           30211377           11383           102400          32011953           11959           107584          32814081           14087           126736          35617777           17783           160000          40020353           20359           183184          42822901           22907           206116          45425813           25819           232324          48226677           26683           240100          49029813           29819           268324          51832881           32887           295936          54435093           35099           315844          56251377           51383           462400          68054133           54139           487204          69876913           76919           692224          83278773           78779           708964          84282177           82183           739600          86083713           83719           753424          868104113          104119          937024          968117877          117883          1060900         1030122033          122039          1098304         1048137393          137399          1236544         1112162677          162683          1464100         1210165377          165383          1488400         1220170293          170299          1532644         1238172501          172507          1552516         1246180341          180347          1623076         1274201301          201307          1811716         1346209153          209159          1882384         1372220273          220279          1982464         1408229121          229127          2062096         1436234901          234907          2114116         1454246677          246683          2220100         1490`

 Posted by Charlie on 2014-01-03 12:47:43

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