(i) Assign 5 distinct values (1 TO 26) to the set (P,R,I,M,E) so that the number
P*R*I*M*E+1 will be prime.
(ii) How many assignments are there that satisfy (i)?
(iii) What are the meaning and the origin of this puzzle's title?
P R I M E product
+1
1 2 3 14 17 1429
1 2 3 14 19 1597
1 2 3 14 23 1933
1 2 3 14 24 2017
1 2 3 15 17 1531
1 2 3 15 18 1621
1 2 3 15 20 1801
1 2 3 15 24 2161
1 2 3 15 25 2251
1 2 3 15 26 2341
1 2 3 16 21 2017
1 2 3 16 22 2113
1 2 3 17 21 2143
1 2 3 17 23 2347
1 2 3 17 25 2551
1 2 3 18 19 2053
1 2 3 18 20 2161
1 2 3 18 21 2269
1 2 3 18 22 2377
1 2 3 18 24 2593
1 2 3 19 20 2281
1 2 3 19 25 2851
1 2 3 20 21 2521
1 2 3 20 25 3001
1 2 3 20 26 3121
1 2 3 22 23 3037
1 2 3 22 24 3169
1 2 3 22 25 3301
1 2 3 22 26 3433
1 2 3 23 24 3313
1 2 4 15 18 2161
1 2 4 15 19 2281
1 2 4 15 21 2521
1 2 4 15 25 3001
1 2 4 15 26 3121
1 2 4 16 21 2689
1 2 4 16 26 3329
1 2 4 17 21 2857
1 2 4 18 22 3169
1 2 4 18 23 3313
1 2 4 18 24 3457
1 2 4 19 20 3041
1 2 4 20 21 3361
1 2 4 20 25 4001
1 2 4 21 22 3697
1 2 4 21 25 4201
1 2 4 22 23 4049
1 2 4 24 25 4801
1 2 4 24 26 4993
1 2 5 16 19 3041
1 2 5 16 21 3361
1 2 5 16 25 4001
1 2 5 17 18 3061
1 2 5 17 21 3571
1 2 5 17 23 3911
1 2 5 17 26 4421
1 2 5 19 24 4561
1 2 5 19 25 4751
1 2 5 20 21 4201
1 2 5 20 24 4801
1 2 5 21 22 4621
1 2 5 21 23 4831
1 2 5 22 24 5281
1 2 5 22 25 5501
1 2 5 23 24 5521
1 2 5 23 26 5981
1 2 6 17 18 3673
1 2 6 17 19 3877
1 2 6 17 25 5101
1 2 6 18 23 4969
1 2 6 19 20 4561
1 2 6 19 21 4789
1 2 6 19 25 5701
1 2 6 20 22 5281
1 2 6 20 23 5521
1 2 6 21 25 6301
1 2 6 21 26 6553
1 2 6 22 23 6073
1 2 6 22 24 6337
1 2 6 23 26 7177
1 2 6 24 26 7489
1 2 7 18 19 4789
1 2 7 18 25 6301
1 2 7 18 26 6553
1 2 7 19 26 6917
1 2 7 20 21 5881
1 2 7 20 25 7001
1 2 7 21 22 6469
1 2 7 21 23 6763
1 2 7 21 24 7057
1 2 7 21 25 7351
1 2 7 22 24 7393
1 2 7 22 26 8009
1 2 7 24 26 8737
1 2 8 19 22 6689
1 2 8 19 24 7297
1 2 8 20 24 7681
1 2 8 21 22 7393
1 2 8 21 26 8737
1 2 8 24 25 9601
1 2 9 20 21 7561
1 2 9 20 24 8641
1 2 9 20 25 9001
1 2 9 21 22 8317
1 2 9 21 26 9829
1 2 9 22 23 9109
1 2 9 22 25 9901
1 2 9 25 26 11701
1 2 10 21 22 9241
1 2 10 21 23 9661
1 2 10 21 25 10501
1 2 10 25 26 13001
1 2 11 22 24 11617
1 2 11 22 25 12101
1 2 11 24 26 13729
1 2 12 23 24 13249
1 2 12 24 25 14401
1 2 12 25 26 15601
1 2 13 24 25 15601
1 2 13 25 26 16901
1 3 4 15 17 3061
1 3 4 16 18 3457
1 3 4 16 25 4801
1 3 4 16 26 4993
1 3 4 17 18 3673
1 3 4 17 19 3877
1 3 4 17 25 5101
1 3 4 18 23 4969
1 3 4 19 20 4561
1 3 4 19 21 4789
1 3 4 19 25 5701
1 3 4 20 22 5281
1 3 4 20 23 5521
1 3 4 21 25 6301
1 3 4 21 26 6553
1 3 4 22 23 6073
1 3 4 22 24 6337
1 3 4 23 26 7177
1 3 4 24 26 7489
1 3 5 16 19 4561
1 3 5 16 20 4801
1 3 5 16 22 5281
1 3 5 16 23 5521
1 3 5 17 18 4591
1 3 5 17 20 5101
1 3 5 17 24 6121
1 3 5 18 23 6211
1 3 5 18 24 6481
1 3 5 19 20 5701
1 3 5 19 22 6271
1 3 5 19 24 6841
1 3 5 19 26 7411
1 3 5 20 21 6301
1 3 5 21 24 7561
1 3 5 21 26 8191
1 3 5 22 23 7591
1 3 5 22 26 8581
1 3 5 23 26 8971
1 3 5 24 25 9001
1 3 6 17 20 6121
1 3 6 17 21 6427
1 3 6 17 22 6733
1 3 6 17 23 7039
1 3 6 18 20 6481
1 3 6 18 22 7129
1 3 6 18 25 8101
1 3 6 19 20 6841
1 3 6 19 23 7867
1 3 6 19 24 8209
1 3 6 19 26 8893
1 3 6 20 21 7561
1 3 6 20 24 8641
1 3 6 20 25 9001
1 3 6 21 22 8317
1 3 6 21 26 9829
1 3 6 22 23 9109
1 3 6 22 25 9901
1 3 6 25 26 11701
1 3 7 18 20 7561
1 3 7 18 22 8317
1 3 7 18 26 9829
1 3 7 19 22 8779
1 3 7 20 21 8821
1 3 7 20 22 9241
1 3 7 20 23 9661
1 3 7 20 25 10501
1 3 7 21 26 11467
1 3 7 22 23 10627
1 3 7 22 25 11551
1 3 7 23 24 11593
1 3 7 24 25 12601
1 3 8 21 23 11593
1 3 8 21 24 12097
1 3 8 21 25 12601
1 3 8 22 26 13729
1 3 8 23 24 13249
1 3 8 24 25 14401
1 3 8 25 26 15601
1 3 9 20 23 12421
1 3 9 22 25 14851
1 3 9 25 26 17551
1 3 10 21 24 15121
1 3 10 21 26 16381
1 3 10 23 24 16561
1 3 10 25 26 19501
1 3 11 22 23 16699
1 3 11 23 24 18217
1 3 11 24 25 19801
1 3 11 24 26 20593
1 3 12 23 26 21529
1 3 12 24 25 21601
1 3 13 24 26 24337
1 4 5 16 17 5441
1 4 5 16 24 7681
1 4 5 17 18 6121
1 4 5 17 22 7481
1 4 5 17 24 8161
1 4 5 17 25 8501
1 4 5 18 19 6841
1 4 5 18 21 7561
1 4 5 18 24 8641
1 4 5 18 25 9001
1 4 5 19 23 8741
1 4 5 20 24 9601
1 4 5 21 22 9241
1 4 5 21 23 9661
1 4 5 21 25 10501
1 4 5 25 26 13001
1 4 6 17 19 7753
1 4 6 17 20 8161
1 4 6 18 19 8209
1 4 6 18 20 8641
1 4 6 18 24 10369
1 4 6 21 23 11593
1 4 6 21 24 12097
1 4 6 21 25 12601
1 4 6 22 26 13729
1 4 6 23 24 13249
1 4 6 24 25 14401
1 4 6 25 26 15601
1 4 7 18 23 11593
1 4 7 18 24 12097
1 4 7 18 25 12601
1 4 7 19 21 11173
1 4 7 20 24 13441
1 4 7 20 26 14561
1 4 7 21 26 15289
1 4 7 22 25 15401
1 4 8 19 20 12161
1 4 8 19 24 14593
1 4 8 19 26 15809
1 4 8 20 21 13441
1 4 8 20 22 14081
1 4 8 20 24 15361
1 4 8 20 25 16001
1 4 8 22 23 16193
1 4 8 23 25 18401
1 4 9 20 21 15121
1 4 9 20 23 16561
1 4 9 21 22 16633
1 4 9 21 23 17389
1 4 9 22 23 18217
1 4 9 22 24 19009
1 4 9 22 25 19801
1 4 9 22 26 20593
1 4 9 23 26 21529
1 4 9 24 25 21601
1 4 10 21 22 18481
1 4 10 21 24 20161
1 4 10 21 25 21001
1 4 10 21 26 21841
1 4 10 22 24 21121
1 4 10 24 25 24001
1 4 11 22 26 25169
1 4 11 23 25 25301
1 4 11 24 26 27457
1 4 12 23 24 26497
1 5 6 17 18 9181
1 5 6 17 21 10711
1 5 6 17 23 11731
1 5 6 17 24 12241
1 5 6 18 23 12421
1 5 6 19 21 11971
1 5 6 19 22 12541
1 5 6 19 24 13681
1 5 6 19 25 14251
1 5 6 19 26 14821
1 5 6 20 21 12601
1 5 6 20 24 14401
1 5 6 20 26 15601
1 5 6 21 24 15121
1 5 6 21 26 16381
1 5 6 23 24 16561
1 5 6 25 26 19501
1 5 7 18 19 11971
1 5 7 18 20 12601
1 5 7 18 24 15121
1 5 7 18 26 16381
1 5 7 19 26 17291
1 5 7 20 22 15401
1 5 7 22 24 18481
1 5 7 22 26 20021
1 5 7 24 25 21001
1 5 7 24 26 21841
1 5 7 25 26 22751
1 5 8 19 25 19001
1 5 8 20 23 18401
1 5 8 21 22 18481
1 5 8 21 24 20161
1 5 8 21 25 21001
1 5 8 21 26 21841
1 5 8 22 24 21121
1 5 8 24 25 24001
1 5 9 20 22 19801
1 5 9 20 24 21601
1 5 9 20 25 22501
1 5 9 21 26 24571
1 5 9 22 24 23761
1 5 9 22 26 25741
1 5 9 23 24 24841
1 5 9 24 26 28081
1 5 9 25 26 29251
1 5 10 21 23 24151
1 5 10 21 25 26251
1 5 10 22 23 25301
1 5 10 23 25 28751
1 5 12 23 25 34501
1 5 12 24 26 37441
1 6 7 18 20 15121
1 6 7 18 21 15877
1 6 7 18 22 16633
1 6 7 18 23 17389
1 6 7 19 21 16759
1 6 7 19 26 20749
1 6 7 20 22 18481
1 6 7 20 24 20161
1 6 7 20 25 21001
1 6 7 20 26 21841
1 6 7 21 23 20287
1 6 7 21 24 21169
1 6 7 21 25 22051
1 6 7 23 25 24151
1 6 7 23 26 25117
1 6 7 24 26 26209
1 6 8 20 21 20161
1 6 8 20 22 21121
1 6 8 20 24 23041
1 6 8 20 25 24001
1 6 8 21 26 26209
1 6 8 22 26 27457
1 6 8 23 24 26497
1 6 9 20 22 23761
1 6 9 20 23 24841
1 6 9 20 26 28081
1 6 9 21 23 26083
1 6 9 21 25 28351
1 6 9 22 24 28513
1 6 9 23 25 31051
1 6 9 24 25 32401
1 6 10 21 24 30241
1 6 10 23 25 34501
1 6 10 24 26 37441
1 6 11 22 24 34849
1 6 11 23 24 36433
1 6 11 23 25 37951
1 6 11 25 26 42901
1 6 12 24 25 43201
1 6 13 24 26 48673
1 6 14 25 26 54601
1 7 8 19 23 24473
1 7 8 19 24 25537
1 7 8 20 24 26881
1 7 8 20 25 28001
1 7 8 21 22 25873
1 7 8 21 25 29401
1 7 8 21 26 30577
1 7 8 22 24 29569
1 7 8 24 25 33601
1 7 9 20 24 30241
1 7 9 22 25 34651
1 7 9 22 26 36037
1 7 9 24 26 39313
1 7 10 21 22 32341
1 7 10 21 23 33811
1 7 10 21 24 35281
1 7 10 22 25 38501
1 7 11 24 26 48049
1 7 11 25 26 50051
1 7 12 25 26 54601
1 7 13 24 25 54601
1 8 9 20 21 30241
1 8 9 20 26 37441
1 8 9 21 26 39313
1 8 9 22 23 36433
1 8 9 24 25 43201
1 8 10 24 26 49921
1 8 12 23 25 55201
1 8 12 24 25 57601
1 8 12 25 26 62401
1 8 13 24 25 62401
1 8 13 25 26 67601
1 9 10 21 24 45361
1 9 10 21 25 47251
1 9 10 22 23 45541
1 9 10 22 24 47521
1 9 10 22 26 51481
1 9 10 23 24 49681
1 9 10 24 25 54001
1 9 11 22 26 56629
1 9 12 23 24 59617
1 9 12 25 26 70201
1 9 13 24 25 70201
1 9 13 24 26 73009
1 9 14 25 26 81901
1 10 11 22 23 55661
1 10 11 22 26 62921
1 10 12 23 25 69001
1 10 12 23 26 71761
1 11 12 24 25 79201
1 11 13 25 26 92951
1 12 13 24 25 93601
1 12 14 25 26 109201
2 3 4 15 17 6121
2 3 4 15 18 6481
2 3 4 15 19 6841
2 3 4 15 21 7561
2 3 4 15 24 8641
2 3 4 15 25 9001
2 3 4 16 17 6529
2 3 4 16 19 7297
2 3 4 16 20 7681
2 3 4 16 25 9601
2 3 4 17 19 7753
2 3 4 17 20 8161
2 3 4 18 19 8209
2 3 4 18 20 8641
2 3 4 18 24 10369
2 3 4 21 23 11593
2 3 4 21 24 12097
2 3 4 21 25 12601
2 3 4 22 26 13729
2 3 4 23 24 13249
2 3 4 24 25 14401
2 3 4 25 26 15601
2 3 5 16 17 8161
2 3 5 16 18 8641
2 3 5 16 20 9601
2 3 5 17 18 9181
2 3 5 17 21 10711
2 3 5 17 23 11731
2 3 5 17 24 12241
2 3 5 18 23 12421
2 3 5 19 21 11971
2 3 5 19 22 12541
2 3 5 19 24 13681
2 3 5 19 25 14251
2 3 5 19 26 14821
2 3 5 20 21 12601
2 3 5 20 24 14401
2 3 5 20 26 15601
2 3 5 21 24 15121
2 3 5 21 26 16381
2 3 5 23 24 16561
2 3 5 25 26 19501
2 3 6 17 20 12241
2 3 6 17 21 12853
2 3 6 17 26 15913
2 3 6 19 20 13681
2 3 6 19 23 15733
2 3 6 19 24 16417
2 3 6 20 21 15121
2 3 6 20 23 16561
2 3 6 21 22 16633
2 3 6 21 23 17389
2 3 6 22 23 18217
2 3 6 22 24 19009
2 3 6 22 25 19801
2 3 6 22 26 20593
2 3 6 23 26 21529
2 3 6 24 25 21601
2 3 7 18 20 15121
2 3 7 18 21 15877
2 3 7 18 22 16633
2 3 7 18 23 17389
2 3 7 19 21 16759
2 3 7 19 26 20749
2 3 7 20 22 18481
2 3 7 20 24 20161
2 3 7 20 25 21001
2 3 7 20 26 21841
2 3 7 21 23 20287
2 3 7 21 24 21169
2 3 7 21 25 22051
2 3 7 23 25 24151
2 3 7 23 26 25117
2 3 7 24 26 26209
2 3 8 20 21 20161
2 3 8 20 22 21121
2 3 8 20 24 23041
2 3 8 20 25 24001
2 3 8 21 26 26209
2 3 8 22 26 27457
2 3 8 23 24 26497
2 3 9 20 22 23761
2 3 9 20 23 24841
2 3 9 20 26 28081
2 3 9 21 23 26083
2 3 9 21 25 28351
2 3 9 22 24 28513
2 3 9 23 25 31051
2 3 9 24 25 32401
2 3 10 21 24 30241
2 3 10 23 25 34501
2 3 10 24 26 37441
2 3 11 22 24 34849
2 3 11 23 24 36433
2 3 11 23 25 37951
2 3 11 25 26 42901
2 3 12 24 25 43201
2 3 13 24 26 48673
2 3 14 25 26 54601
2 4 5 16 19 12161
2 4 5 16 21 13441
2 4 5 16 22 14081
2 4 5 16 24 15361
2 4 5 16 25 16001
2 4 5 17 18 12241
2 4 5 17 21 14281
2 4 5 17 23 15641
2 4 5 17 26 17681
2 4 5 18 19 13681
2 4 5 18 20 14401
2 4 5 18 21 15121
2 4 5 18 23 16561
2 4 5 19 25 19001
2 4 5 20 23 18401
2 4 5 21 22 18481
2 4 5 21 24 20161
2 4 5 21 25 21001
2 4 5 21 26 21841
2 4 5 22 24 21121
2 4 5 24 25 24001
2 4 6 17 21 17137
2 4 6 18 19 16417
2 4 6 18 22 19009
2 4 6 18 25 21601
2 4 6 20 21 20161
2 4 6 20 22 21121
2 4 6 20 24 23041
2 4 6 20 25 24001
2 4 6 21 26 26209
2 4 6 22 26 27457
2 4 6 23 24 26497
2 4 7 18 20 20161
2 4 7 18 21 21169
2 4 7 18 26 26209
2 4 7 19 23 24473
2 4 7 19 24 25537
2 4 7 20 24 26881
2 4 7 20 25 28001
2 4 7 21 22 25873
2 4 7 21 25 29401
2 4 7 21 26 30577
2 4 7 22 24 29569
2 4 7 24 25 33601
2 4 8 19 21 25537
2 4 8 20 21 26881
2 4 8 21 22 29569
2 4 8 21 24 32257
2 4 8 21 25 33601
2 4 8 22 25 35201
2 4 8 23 26 38273
2 4 8 24 26 39937
2 4 9 20 21 30241
2 4 9 20 26 37441
2 4 9 21 26 39313
2 4 9 22 23 36433
2 4 9 24 25 43201
2 4 10 24 26 49921
2 4 12 23 25 55201
2 4 12 24 25 57601
2 4 12 25 26 62401
2 4 13 24 25 62401
2 4 13 25 26 67601
2 5 6 17 19 19381
2 5 6 17 22 22441
2 5 6 17 24 24481
2 5 6 18 19 20521
2 5 6 18 20 21601
2 5 6 18 22 23761
2 5 6 18 23 24841
2 5 6 18 26 28081
2 5 6 19 24 27361
2 5 6 19 26 29641
2 5 6 21 24 30241
2 5 6 23 25 34501
2 5 6 24 26 37441
2 5 7 18 24 30241
2 5 7 20 21 29401
2 5 7 20 24 33601
2 5 7 21 22 32341
2 5 7 21 23 33811
2 5 7 21 24 35281
2 5 7 22 25 38501
2 5 8 19 23 34961
2 5 8 19 26 39521
2 5 8 20 21 33601
2 5 8 20 22 35201
2 5 8 24 26 49921
2 5 9 20 24 43201
2 5 9 21 24 45361
2 5 9 21 25 47251
2 5 9 22 23 45541
2 5 9 22 24 47521
2 5 9 22 26 51481
2 5 9 23 24 49681
2 5 9 24 25 54001
2 5 10 21 25 52501
2 5 10 21 26 54601
2 5 10 22 25 55001
2 5 10 23 24 55201
2 5 10 24 26 62401
2 5 11 22 23 55661
2 5 11 22 26 62921
2 5 12 23 25 69001
2 5 12 23 26 71761
2 6 7 18 19 28729
2 6 7 18 20 30241
2 6 7 18 26 39313
2 6 7 19 23 36709
2 6 7 19 25 39901
2 6 7 20 21 35281
2 6 7 21 24 42337
2 6 7 21 25 44101
2 6 7 22 26 48049
2 6 7 25 26 54601
2 6 8 19 22 40129
2 6 8 19 23 41953
2 6 8 19 24 43777
2 6 8 20 26 49921
2 6 8 23 25 55201
2 6 8 24 25 57601
2 6 8 25 26 62401
2 6 9 20 21 45361
2 6 9 20 22 47521
2 6 9 20 23 49681
2 6 9 20 25 54001
2 6 9 21 25 56701
2 6 9 23 24 59617
2 6 9 25 26 70201
2 6 10 21 22 55441
2 6 10 21 26 65521
2 6 10 22 24 63361
2 6 10 23 25 69001
2 6 10 23 26 71761
2 6 11 22 24 69697
2 6 11 24 25 79201
2 6 12 23 26 86113
2 6 12 25 26 93601
2 6 13 24 25 93601
2 6 14 25 26 109201
2 7 8 19 22 46817
2 7 8 19 25 53201
2 7 8 20 21 47041
2 7 8 20 23 51521
2 7 8 21 26 61153
2 7 8 23 26 66977
2 7 9 20 22 55441
2 7 9 20 26 65521
2 7 9 21 23 60859
2 7 9 22 24 66529
2 7 9 22 26 72073
2 7 9 25 26 81901
2 7 10 21 26 76441
2 7 10 22 23 70841
2 7 11 22 25 84701
2 7 11 23 24 85009
2 7 11 24 25 92401
2 7 11 24 26 96097
2 7 12 23 24 92737
2 7 12 23 25 96601
2 7 12 24 25 100801
2 7 12 25 26 109201
2 7 13 24 25 109201
2 8 9 20 22 63361
2 8 9 21 22 66529
2 8 9 21 24 72577
2 8 9 22 25 79201
2 8 9 23 26 86113
2 8 9 25 26 93601
2 8 10 22 24 84481
2 8 10 22 25 88001
2 8 10 23 24 88321
2 8 10 24 25 96001
2 8 11 22 23 89057
2 8 11 22 26 100673
2 8 11 24 25 105601
2 8 12 24 25 115201
2 8 12 24 26 119809
2 8 13 24 26 129793
2 8 14 25 26 145601
2 9 10 22 23 91081
2 9 10 23 26 107641
2 9 11 22 23 100189
2 9 11 23 24 109297
2 9 11 24 25 118801
2 9 11 24 26 123553
2 9 12 23 24 119233
2 9 12 23 26 129169
2 9 12 25 26 140401
2 9 13 24 25 140401
2 10 11 22 25 121001
2 10 11 23 24 121441
2 10 11 23 26 131561
2 10 11 24 25 132001
2 11 14 25 26 200201
2 12 14 25 26 218401
3 4 5 16 21 20161
3 4 5 16 22 21121
3 4 5 16 24 23041
3 4 5 16 25 24001
3 4 5 17 19 19381
3 4 5 17 22 22441
3 4 5 17 24 24481
3 4 5 18 19 20521
3 4 5 18 20 21601
3 4 5 18 22 23761
3 4 5 18 23 24841
3 4 5 18 26 28081
3 4 5 19 24 27361
3 4 5 19 26 29641
3 4 5 21 24 30241
3 4 5 23 25 34501
3 4 5 24 26 37441
3 4 6 17 20 24481
3 4 6 18 22 28513
3 4 6 18 25 32401
3 4 6 19 20 27361
3 4 6 19 21 28729
3 4 6 19 22 30097
3 4 6 19 24 32833
3 4 6 19 26 35569
3 4 6 20 21 30241
3 4 6 20 26 37441
3 4 6 21 26 39313
3 4 6 22 23 36433
3 4 6 24 25 43201
3 4 7 18 19 28729
3 4 7 18 20 30241
3 4 7 18 26 39313
3 4 7 19 23 36709
3 4 7 19 25 39901
3 4 7 20 21 35281
3 4 7 21 24 42337
3 4 7 21 25 44101
3 4 7 22 26 48049
3 4 7 25 26 54601
3 4 8 19 22 40129
3 4 8 19 23 41953
3 4 8 19 24 43777
3 4 8 20 26 49921
3 4 8 23 25 55201
3 4 8 24 25 57601
3 4 8 25 26 62401
3 4 9 20 21 45361
3 4 9 20 22 47521
3 4 9 20 23 49681
3 4 9 20 25 54001
3 4 9 21 25 56701
3 4 9 23 24 59617
3 4 9 25 26 70201
3 4 10 21 22 55441
3 4 10 21 26 65521
3 4 10 22 24 63361
3 4 10 23 25 69001
3 4 10 23 26 71761
3 4 11 22 24 69697
3 4 11 24 25 79201
3 4 12 23 26 86113
3 4 12 25 26 93601
3 4 13 24 25 93601
3 4 14 25 26 109201
3 5 6 17 18 27541
3 5 6 17 24 36721
3 5 6 18 19 30781
3 5 6 18 20 32401
3 5 6 19 21 35911
3 5 6 19 25 42751
3 5 6 20 24 43201
3 5 6 21 24 45361
3 5 6 21 25 47251
3 5 6 22 23 45541
3 5 6 22 24 47521
3 5 6 22 26 51481
3 5 6 23 24 49681
3 5 6 24 25 54001
3 5 7 18 19 35911
3 5 7 18 24 45361
3 5 7 18 25 47251
3 5 7 19 20 39901
3 5 7 19 22 43891
3 5 7 19 24 47881
3 5 7 19 26 51871
3 5 7 20 21 44101
3 5 7 20 25 52501
3 5 7 20 26 54601
3 5 7 21 26 57331
3 5 7 22 24 55441
3 5 7 22 25 57751
3 5 7 23 26 62791
3 5 7 24 26 65521
3 5 8 19 21 47881
3 5 8 19 24 54721
3 5 8 19 26 59281
3 5 8 20 23 55201
3 5 8 20 24 57601
3 5 8 20 26 62401
3 5 8 21 22 55441
3 5 8 21 26 65521
3 5 8 22 24 63361
3 5 8 23 25 69001
3 5 8 23 26 71761
3 5 9 20 21 56701
3 5 9 20 26 70201
3 5 9 21 24 68041
3 5 9 22 23 68311
3 5 9 23 24 74521
3 5 9 24 25 81001
3 5 9 25 26 87751
3 5 10 21 26 81901
3 5 10 22 24 79201
3 5 10 24 25 90001
3 5 10 24 26 93601
3 5 10 25 26 97501
3 5 11 22 24 87121
3 5 11 23 24 91081
3 5 11 25 26 107251
3 5 12 23 26 107641
3 5 13 25 26 126751
3 5 14 25 26 136501
3 6 7 18 19 43093
3 6 7 18 20 45361
3 6 7 18 21 47629
3 6 7 18 25 56701
3 6 7 19 20 47881
3 6 7 19 24 57457
3 6 7 20 22 55441
3 6 7 20 26 65521
3 6 7 21 23 60859
3 6 7 22 24 66529
3 6 7 22 26 72073
3 6 7 25 26 81901
3 6 8 19 20 54721
3 6 8 19 21 57457
3 6 8 19 23 62929
3 6 8 20 22 63361
3 6 8 21 22 66529
3 6 8 21 24 72577
3 6 8 22 25 79201
3 6 8 23 26 86113
3 6 8 25 26 93601
3 6 9 20 21 68041
3 6 9 20 23 74521
3 6 9 20 24 77761
3 6 9 20 25 81001
3 6 9 21 24 81649
3 6 9 22 23 81973
3 6 9 22 25 89101
3 6 9 23 25 93151
3 6 9 24 26 101089
3 6 10 22 23 91081
3 6 10 23 26 107641
3 6 11 22 23 100189
3 6 11 23 24 109297
3 6 11 24 25 118801
3 6 11 24 26 123553
3 6 12 23 24 119233
3 6 12 23 26 129169
3 6 12 25 26 140401
3 6 13 24 25 140401
3 7 8 19 20 63841
3 7 8 19 21 67033
3 7 8 19 23 73417
3 7 8 19 25 79801
3 7 8 21 22 77617
3 7 8 21 24 84673
3 7 8 22 23 85009
3 7 8 22 25 92401
3 7 8 22 26 96097
3 7 8 23 24 92737
3 7 8 23 25 96601
3 7 8 24 25 100801
3 7 8 25 26 109201
3 7 9 21 24 95257
3 7 9 22 24 99793
3 7 9 22 25 103951
3 7 9 22 26 108109
3 7 9 23 26 113023
3 7 9 24 26 117937
3 7 10 21 22 97021
3 7 10 21 25 110251
3 7 10 21 26 114661
3 7 10 22 23 106261
3 7 10 22 24 110881
3 7 10 22 26 120121
3 7 10 24 25 126001
3 7 10 24 26 131041
3 7 10 25 26 136501
3 7 11 22 25 127051
3 7 11 23 26 138139
3 7 11 25 26 150151
3 7 12 23 26 150697
3 7 12 24 25 151201
3 7 13 24 26 170353
3 8 9 20 24 103681
3 8 9 21 22 99793
3 8 9 21 26 117937
3 8 9 22 23 109297
3 8 9 22 25 118801
3 8 9 22 26 123553
3 8 9 23 24 119233
3 8 9 23 26 129169
3 8 9 25 26 140401
3 8 10 21 22 110881
3 8 10 21 25 126001
3 8 10 21 26 131041
3 8 10 22 23 121441
3 8 10 22 25 132001
3 8 11 22 24 139393
3 8 11 22 26 151009
3 8 12 23 25 165601
3 8 12 24 25 172801
3 8 14 25 26 218401
3 9 10 21 23 130411
3 9 10 22 23 136621
3 9 10 22 25 148501
3 9 10 23 25 155251
3 9 10 23 26 161461
3 9 10 24 26 168481
3 9 11 22 24 156817
3 9 11 22 25 163351
3 9 11 25 26 193051
3 9 12 23 25 186301
3 9 12 25 26 210601
3 9 13 24 25 210601
3 10 11 22 24 174241
3 10 11 22 25 181501
3 10 11 23 26 197341
3 10 13 25 26 253501
3 10 14 25 26 273001
3 11 12 25 26 257401
3 11 13 24 25 257401
3 11 14 25 26 300301
4 5 6 17 18 36721
4 5 6 17 20 40801
4 5 6 17 21 42841
4 5 6 17 25 51001
4 5 6 18 20 43201
4 5 6 18 21 45361
4 5 6 18 22 47521
4 5 6 18 23 49681
4 5 6 18 25 54001
4 5 6 19 21 47881
4 5 6 19 24 54721
4 5 6 19 26 59281
4 5 6 20 23 55201
4 5 6 20 24 57601
4 5 6 20 26 62401
4 5 6 21 22 55441
4 5 6 21 26 65521
4 5 6 22 24 63361
4 5 6 23 25 69001
4 5 6 23 26 71761
4 5 7 18 19 47881
4 5 7 18 22 55441
4 5 7 18 26 65521
4 5 7 19 20 53201
4 5 7 19 24 63841
4 5 7 20 25 70001
4 5 7 21 26 76441
4 5 7 22 23 70841
4 5 8 19 21 63841
4 5 8 19 25 76001
4 5 8 20 24 76801
4 5 8 22 24 84481
4 5 8 22 25 88001
4 5 8 23 24 88321
4 5 8 24 25 96001
4 5 9 20 22 79201
4 5 9 20 25 90001
4 5 9 20 26 93601
4 5 9 22 23 91081
4 5 9 23 26 107641
4 5 10 21 22 92401
4 5 10 21 23 96601
4 5 10 21 24 100801
4 5 10 21 26 109201
4 5 10 22 24 105601
4 5 10 23 25 115001
4 5 11 22 25 121001
4 5 11 23 24 121441
4 5 11 23 26 131561
4 5 11 24 25 132001
4 6 7 18 19 57457
4 6 7 18 22 66529
4 6 7 18 24 72577
4 6 7 19 20 63841
4 6 7 19 21 67033
4 6 7 19 23 73417
4 6 7 19 25 79801
4 6 7 21 22 77617
4 6 7 21 24 84673
4 6 7 22 23 85009
4 6 7 22 25 92401
4 6 7 22 26 96097
4 6 7 23 24 92737
4 6 7 23 25 96601
4 6 7 24 25 100801
4 6 7 25 26 109201
4 6 8 19 24 87553
4 6 8 19 26 94849
4 6 8 20 22 84481
4 6 8 20 23 88321
4 6 8 20 25 96001
4 6 8 21 23 92737
4 6 8 21 24 96769
4 6 8 21 25 100801
4 6 8 22 24 101377
4 6 8 22 25 105601
4 6 8 24 25 115201
4 6 8 24 26 119809
4 6 9 20 24 103681
4 6 9 21 22 99793
4 6 9 21 26 117937
4 6 9 22 23 109297
4 6 9 22 25 118801
4 6 9 22 26 123553
4 6 9 23 24 119233
4 6 9 23 26 129169
4 6 9 25 26 140401
4 6 10 21 22 110881
4 6 10 21 25 126001
4 6 10 21 26 131041
4 6 10 22 23 121441
4 6 10 22 25 132001
4 6 11 22 24 139393
4 6 11 22 26 151009
4 6 12 23 25 165601
4 6 12 24 25 172801
4 6 14 25 26 218401
4 7 8 19 20 85121
4 7 8 20 22 98561
4 7 8 21 23 108193
4 7 8 22 24 118273
4 7 8 24 25 134401
4 7 8 25 26 145601
4 7 9 20 22 110881
4 7 9 20 25 126001
4 7 9 20 26 131041
4 7 9 21 26 137593
4 7 9 23 26 150697
4 7 9 24 25 151201
4 7 10 21 22 129361
4 7 10 21 23 135241
4 7 10 21 24 141121
4 7 10 22 25 154001
4 7 10 23 26 167441
4 7 10 24 26 174721
4 7 11 22 23 155849
4 7 11 23 25 177101
4 7 11 24 26 192193
4 7 11 25 26 200201
4 7 12 23 25 193201
4 7 12 23 26 200929
4 7 12 25 26 218401
4 7 13 24 25 218401
4 8 9 20 24 138241
4 8 9 21 25 151201
4 8 9 23 25 165601
4 8 9 24 25 172801
4 8 10 21 24 161281
4 8 10 21 26 174721
4 8 10 22 23 161921
4 8 10 22 26 183041
4 8 10 23 24 176641
4 8 10 25 26 208001
4 8 11 22 25 193601
4 8 11 24 26 219649
4 8 12 23 24 211969
4 9 10 21 26 196561
4 9 11 22 24 209089
4 9 11 25 26 257401
4 9 12 23 25 248401
4 9 12 23 26 258337
4 9 12 24 25 259201
4 10 11 25 26 286001
4 10 12 23 24 264961
4 10 12 24 26 299521
4 11 12 23 24 291457
4 11 12 24 25 316801
4 11 12 24 26 329473
4 11 13 24 26 356929
4 12 14 25 26 436801
4 13 14 25 26 473201
5 6 7 18 19 71821
5 6 7 19 20 79801
5 6 7 19 21 83791
5 6 7 19 23 91771
5 6 7 20 22 92401
5 6 7 20 23 96601
5 6 7 20 24 100801
5 6 7 20 26 109201
5 6 7 21 22 97021
5 6 7 21 25 110251
5 6 7 21 26 114661
5 6 7 22 23 106261
5 6 7 22 24 110881
5 6 7 22 26 120121
5 6 7 24 25 126001
5 6 7 24 26 131041
5 6 7 25 26 136501
5 6 8 19 24 109441
5 6 8 19 25 114001
5 6 8 20 21 100801
5 6 8 20 22 105601
5 6 8 20 24 115201
5 6 8 21 22 110881
5 6 8 21 25 126001
5 6 8 21 26 131041
5 6 8 22 23 121441
5 6 8 22 25 132001
5 6 9 20 22 118801
5 6 9 20 26 140401
5 6 9 21 23 130411
5 6 9 22 23 136621
5 6 9 22 25 148501
5 6 9 23 25 155251
5 6 9 23 26 161461
5 6 9 24 26 168481
5 6 10 21 24 151201
5 6 10 22 25 165001
5 6 10 23 24 165601
5 6 10 24 25 180001
5 6 11 22 24 174241
5 6 11 22 25 181501
5 6 11 23 26 197341
5 6 13 25 26 253501
5 6 14 25 26 273001
5 7 8 19 21 111721
5 7 8 19 22 117041
5 7 8 19 24 127681
5 7 8 20 24 134401
5 7 8 20 26 145601
5 7 8 21 22 129361
5 7 8 21 23 135241
5 7 8 21 24 141121
5 7 8 22 25 154001
5 7 8 23 26 167441
5 7 8 24 26 174721
5 7 9 20 24 151201
5 7 9 21 22 145531
5 7 9 21 24 158761
5 7 9 22 26 180181
5 7 9 24 26 196561
5 7 9 25 26 204751
5 7 10 21 24 176401
5 7 10 22 23 177101
5 7 10 22 26 200201
5 7 10 23 24 193201
5 7 10 23 25 201251
5 7 10 24 26 218401
5 7 10 25 26 227501
5 7 11 24 25 231001
5 7 12 23 24 231841
5 7 12 24 25 252001
5 7 12 25 26 273001
5 7 13 24 25 273001
5 7 13 25 26 295751
5 8 9 20 21 151201
5 8 9 20 23 165601
5 8 9 20 24 172801
5 8 9 20 25 180001
5 8 9 21 26 196561
5 8 10 21 23 193201
5 8 10 21 26 218401
5 8 10 23 26 239201
5 8 11 25 26 286001
5 8 12 23 24 264961
5 8 12 24 26 299521
5 9 10 21 23 217351
5 9 10 22 25 247501
5 9 10 22 26 257401
5 9 10 23 24 248401
5 9 10 24 25 270001
5 9 11 23 26 296011
5 9 11 25 26 321751
5 9 12 23 25 310501
5 9 12 23 26 322921
5 9 12 24 26 336961
5 9 13 25 26 380251
5 10 11 23 26 328901
5 10 12 23 25 345001
5 10 12 25 26 390001
5 10 13 24 25 390001
5 11 12 23 24 364321
5 11 12 23 25 379501
5 11 12 24 25 396001
5 11 12 24 26 411841
5 11 14 25 26 500501
5 12 13 24 25 468001
5 12 13 24 26 486721
5 12 14 25 26 546001
6 7 8 19 20 127681
6 7 8 19 22 140449
6 7 8 19 23 146833
6 7 8 20 21 141121
6 7 8 20 24 161281
6 7 8 20 26 174721
6 7 8 21 23 162289
6 7 8 21 25 176401
6 7 8 22 24 177409
6 7 8 22 26 192193
6 7 8 23 25 193201
6 7 8 23 26 200929
6 7 8 25 26 218401
6 7 9 20 21 158761
6 7 9 20 26 196561
6 7 9 21 22 174637
6 7 9 22 26 216217
6 7 9 23 24 208657
6 7 9 23 25 217351
6 7 10 21 24 211681
6 7 10 21 26 229321
6 7 10 22 25 231001
6 7 10 23 24 231841
6 7 10 24 25 252001
6 7 10 25 26 273001
6 7 11 23 26 276277
6 7 11 25 26 300301
6 7 12 23 24 278209
6 7 12 24 26 314497
6 8 9 21 23 208657
6 8 9 22 24 228097
6 8 9 23 25 248401
6 8 9 23 26 258337
6 8 9 24 25 259201
6 8 10 21 23 231841
6 8 10 21 24 241921
6 8 10 21 25 252001
6 8 10 23 24 264961
6 8 10 24 26 299521
6 8 11 23 24 291457
6 8 11 24 25 316801
6 8 11 24 26 329473
6 8 12 24 25 345601
6 8 14 25 26 436801
6 9 10 21 25 283501
6 9 10 22 24 285121
6 9 10 23 25 310501
6 9 10 23 26 322921
6 9 10 24 26 336961
6 9 11 22 25 326701
6 9 11 22 26 339769
6 9 11 23 24 327889
6 9 13 24 26 438049
6 10 11 22 26 377521
6 10 11 23 24 364321
6 10 11 23 25 379501
6 10 11 24 25 396001
6 10 11 24 26 411841
6 10 12 24 25 432001
6 10 12 25 26 468001
6 10 13 24 25 468001
6 10 13 24 26 486721
6 10 14 25 26 546001
6 11 12 23 25 455401
6 11 12 23 26 473617
6 11 14 25 26 600601
6 12 13 25 26 608401
7 8 9 20 21 211681
7 8 9 20 23 231841
7 8 9 20 24 241921
7 8 9 20 25 252001
7 8 9 21 23 243433
7 8 9 21 25 264601
7 8 9 23 24 278209
7 8 9 24 26 314497
7 8 10 21 22 258721
7 8 10 21 24 282241
7 8 10 21 25 294001
7 8 10 21 26 305761
7 8 10 23 24 309121
7 8 10 23 25 322001
7 8 11 22 24 325249
7 8 11 23 26 368369
7 8 12 23 25 386401
7 8 12 24 26 419329
7 8 12 25 26 436801
7 8 13 24 25 436801
7 8 13 25 26 473201
7 9 10 22 23 318781
7 9 10 22 24 332641
7 9 10 22 25 346501
7 9 10 24 26 393121
7 9 11 24 25 415801
7 9 11 24 26 432433
7 9 11 25 26 450451
7 9 12 24 25 453601
7 9 13 24 26 511057
7 10 11 22 23 389621
7 10 11 22 24 406561
7 10 11 22 26 440441
7 10 11 25 26 500501
7 10 12 23 26 502321
7 10 12 24 25 504001
7 10 12 25 26 546001
7 10 13 24 25 546001
7 10 13 24 26 567841
7 10 14 25 26 637001
7 11 12 23 24 510049
7 11 12 23 26 552553
7 11 12 24 26 576577
7 11 12 25 26 600601
7 11 13 24 25 600601
7 12 13 24 26 681409
7 13 14 25 26 828101
8 9 10 21 22 332641
8 9 10 21 26 393121
8 9 10 22 23 364321
8 9 10 22 25 396001
8 9 10 22 26 411841
8 9 10 24 25 432001
8 9 10 25 26 468001
8 9 11 22 23 400753
8 9 11 22 24 418177
8 9 11 23 25 455401
8 9 11 23 26 473617
8 9 12 23 24 476929
8 9 12 23 26 516673
8 9 13 25 26 608401
8 10 11 24 25 528001
8 10 11 24 26 549121
8 10 12 23 25 552001
8 10 12 23 26 574081
8 10 12 24 25 576001
8 10 13 24 26 648961
8 11 14 25 26 800801
8 12 13 24 25 748801
9 10 11 22 25 544501
9 10 11 23 25 569251
9 10 11 24 26 617761
9 10 12 24 26 673921
9 10 14 25 26 819001
9 12 13 24 26 876097
9 12 14 25 26 982801
10 11 12 23 25 759001
10 11 12 25 26 858001
10 11 13 24 25 858001
10 11 13 24 26 892321
10 11 13 25 26 929501
11 12 13 24 25 1029601
11 12 14 25 26 1201201
1362 such quintuples form the requested primes; this is out of the C(26,5)=65780 possible quintuples.
The actual number of assignments is 1362*5! = 163440, but then we need to use P(26,5) for comparison. P(26,5) = 7893600.
DefDbl A-Z
Dim crlf$, used(26)
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
For p = 1 To 26
used(p) = 1
For r = p + 1 To 26
If used(r) = 0 Then
used(r) = 1
For i = r + 1 To 26
If used(i) = 0 Then
used(i) = 1
For m = i + 11 To 26
If used(m) = 0 Then
used(r) = 1
For e = m + 1 To 26
If used(e) = 0 Then
used(e) = 1
pr = p * r * i * m * e + 1
If prmdiv(pr) = pr Then
Text1.Text = Text1.Text & Str(p) & Str(r) & Str(i) & Str(m) & Str(e) & Str(pr) & crlf
ct = ct + 1
End If
DoEvents
used(e) = 0
End If
Next
used(m) = 0
End If
Next
used(i) = 0
End If
Next
used(r) = 0
End If
Next
used(p) = 0
Next
Text1.Text = Text1.Text & crlf & ct & " done"
End Sub
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
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Posted by Charlie
on 2017-10-17 16:16:32 |
computer solution
