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?
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 4
53 59 484 22
277 283 2500 50
373 379 3364 58
641 647 5776 76
821 827 7396 86
1393 1399 12544 112
3061 3067 27556 166
3761 3767 33856 184
4993 4999 44944 212
6293 6299 56644 238
7861 7867 70756 266
9473 9479 85264 292
10133 10139 91204 302
11377 11383 102400 320
11953 11959 107584 328
14081 14087 126736 356
17777 17783 160000 400
20353 20359 183184 428
22901 22907 206116 454
25813 25819 232324 482
26677 26683 240100 490
29813 29819 268324 518
32881 32887 295936 544
35093 35099 315844 562
51377 51383 462400 680
54133 54139 487204 698
76913 76919 692224 832
78773 78779 708964 842
82177 82183 739600 860
83713 83719 753424 868
104113 104119 937024 968
117877 117883 1060900 1030
122033 122039 1098304 1048
137393 137399 1236544 1112
162677 162683 1464100 1210
165377 165383 1488400 1220
170293 170299 1532644 1238
172501 172507 1552516 1246
180341 180347 1623076 1274
201301 201307 1811716 1346
209153 209159 1882384 1372
220273 220279 1982464 1408
229121 229127 2062096 1436
234901 234907 2114116 1454
246677 246683 2220100 1490
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Posted by Charlie
on 2014-01-03 12:47:43 |
computer solution
