Voici les plus grandes graines pour les premiers inférieurs à 501089,

classées par graines décroissantes.

On pourra remarquer 5881 très petit pour une graine de 31.

88079 encore est remarquable, pour une graine aussi élevée, son abondance l'est aussi.

(c'est d'ailleurs étonnant, j'espère que ce n'est pas dû à une erreur de calcul ;-)

Le vide reste patent pour les graines 27, 25 et 24.
Premier
Graine
Abondance
Numérateur
Dénominateur
Décomposition du Premier - 1
110881
69
20,779220779
16
77
2^5 * 3^2 * 5 * 7 * 11
336361
58
26,65715305
3736
14015
2^3 * 3 * 5 * 2803
471769
57
30,286072815
17860
58971
2^3 * 3 * 11 * 1787
459841
55
26,610995129
1912
7185
2^6 * 3 * 5 * 479
161831
53
39,99752827
32364
80915
2 * 5 * 16183
129361
52
20,779220779
16
77
2^4 * 3 * 5 * 7^2 * 11
322999
51
29,721546263
16000
53833
2 * 3 * 13 * 41 * 101
374761
47
26,589817483
1384
5205
2^3 * 3^3 * 5 * 347
275641
47
26,655057321
9184
34455
2^3 * 3 * 5 * 2297
273001
46
21,098901099
96
455
2^3 * 3 * 5^3 * 7 * 13
380881
44
25,507246377
88
345
2^4 * 3^2 * 5 * 23^2
71761
44
23,545150502
352
1495
2^4 * 3 * 5 * 13 * 23
346441
44
26,657429858
3848
14435
2^3 * 3 * 5 * 2887
329281
43
22,857142857
8
35
2^6 * 3 * 5 * 7^3
140617
43
27,649769585
60
217
2^3 * 3^4 * 7 * 31
225289
43
28,379674017
296
1043
2^3 * 3^3 * 7 * 149
352489
43
31,538094914
4632
14687
2^3 * 3 * 19 * 773
166871
43
34,517888176
5760
16687
2 * 5 * 11 * 37 * 41
475151
43
33,942965379
16128
47515
2 * 5^2 * 13 * 17 * 43
95471
43
39,995810202
19092
47735
2 * 5 * 9547
104711
43
38,781396237
20304
52355
2 * 5 * 37 * 283
366791
43
39,023964666
71568
183395
2 * 5 * 43 * 853
156601
41
25,747126437
112
435
2^3 * 3^3 * 5^2 * 29
185641
41
19,85778927
1536
7735
2^3 * 3 * 5 * 7 * 13 * 17
266137
41
30,733158986
3408
11089
2^3 * 3 * 13 * 853
375311
41
36,910287496
5328
14435
2 * 5 * 13 * 2887
284231
41
39,010660381
11088
28423
2 * 5 * 43 * 661
494471
41
39,638400712
19600
49447
2 * 5 * 197 * 251
325249
39
25,974025974
20
77
2^7 * 3 * 7 * 11^2
388081
39
20,779220779
16
77
2^4 * 3^2 * 5 * 7^2 * 11
264961
39
25,507246377
88
345
2^8 * 3^2 * 5 * 23
462841
39
20,907441016
576
2755
2^3 * 3 * 5 * 7 * 19 * 29
166031
39
39,997590797
33204
83015
2 * 5 * 16603
450071
39
39,999111249
90012
225035
2 * 5 * 45007
55441
38
20,779220779
16
77
2^4 * 3^2 * 5 * 7 * 11
497351
38
33,103448276
48
145
2 * 5^2 * 7^3 * 29
138889
38
33,281493002
214
643
2^3 * 3^3 * 643
469561
38
20,60822898
576
2795
2^3 * 3 * 5 * 7 * 13 * 43
441169
38
26,11250136
2400
9191
2^4 * 3 * 7 * 13 * 101
343561
38
22,801257422
3264
14315
2^3 * 3 * 5 * 7 * 409
63361
37
24,242424242
8
33
2^7 * 3^2 * 5 * 11
97441
37
22,068965517
32
145
2^5 * 3 * 5 * 7 * 29
36721
37
25,098039216
64
255
2^4 * 3^3 * 5 * 17
314161
37
19,556913675
256
1309
2^4 * 3 * 5 * 7 * 11 * 17
51361
37
26,417445483
424
1605
2^5 * 3 * 5 * 107
129529
37
28,460255698
512
1799
2^3 * 3^2 * 7 * 257
496609
37
28,532766286
1476
5173
2^5 * 3 * 7 * 739
387721
37
26,592386258
1432
5385
2^3 * 3^3 * 5 * 359
201769
37
28,547638872
2400
8407
2^3 * 3 * 7 * 1201
171889
37
33,324024946
3580
10743
2^4 * 3 * 3581
343081
37
26,638684855
3808
14295
2^3 * 3^2 * 5 * 953
132169
37
33,327280431
5506
16521
2^3 * 3 * 5507
190537
37
31,305370114
7456
23817
2^3 * 3 * 17 * 467
333791
37
38,587135624
12880
33379
2 * 5 * 29 * 1151
422231
37
39,999052649
84444
211115
2 * 5 * 42223
493919
37
46,180945015
114048
246959
2 * 17 * 73 * 199
64609
35
33,283803863
224
673
2^5 * 3 * 673
93481
35
24,646983312
192
779
2^3 * 3 * 5 * 19 * 41
319057
35
30,008525149
352
1173
2^4 * 3 * 17^2 * 23
334777
35
28,905297871
4032
13949
2^3 * 3 * 13 * 29 * 37
290041
35
26,655633706
9664
36255
2^3 * 3 * 5 * 2417
155521
34
26,666666667
4
15
2^7 * 3^5 * 5
285121
34
24,242424242
8
33
2^6 * 3^4 * 5 * 11
92401
34
20,779220779
16
77
2^4 * 3 * 5^2 * 7 * 11
493291
34
22,068965517
32
145
2 * 3^5 * 5 * 7 * 29
88321
34
25,507246377
88
345
2^8 * 3 * 5 * 23
290161
34
23,82133995
96
403
2^4 * 3^2 * 5 * 13 * 31
379681
34
22,654867257
128
565
2^5 * 3 * 5 * 7 * 113
48889
34
28,276877761
192
679
2^3 * 3^2 * 7 * 97
229681
34
23,406478579
224
957
2^4 * 3^2 * 5 * 11 * 29
407521
34
26,572438163
376
1415
2^5 * 3^2 * 5 * 283
289249
34
31,640668216
2860
9039
2^5 * 3 * 23 * 131
284881
34
26,644201067
4744
17805
2^4 * 3 * 5 * 1187
233941
34
22,816106694
4448
19495
2^2 * 3 * 5 * 7 * 557
353929
34
33,331072987
14746
44241
2^3 * 3 * 14747
316681
33
20,371352785
384
1885
2^3 * 3 * 5 * 7 * 13 * 29
268969
33
28,553582582
3200
11207
2^3 * 3 * 7 * 1601
275263
33
30,760511803
14112
45877
2 * 3 * 13 * 3529
492911
33
36,355521292
17920
49291
2 * 5 * 11 * 4481
101089
31
30,769230769
4
13
2^5 * 3^5 * 13
316801
31
24,242424242
8
33
2^7 * 3^2 * 5^2 * 11
5881
31
22,857142857
8
35
2^3 * 3 * 5 * 7^2
415801
31
20,779220779
16
77
2^3 * 3^3 * 5^2 * 7 * 11
102001
31
25,098039216
64
255
2^4 * 3 * 5^3 * 17
390151
31
25,098039216
64
255
2 * 3^3 * 5^2 * 17^2
275521
31
22,299651568
64
287
2^6 * 3 * 5 * 7 * 41
43801
31
26,301369863
96
365
2^3 * 3 * 5^2 * 73
141961
31
21,098901099
96
455
2^3 * 3 * 5 * 7 * 13^2
92569
31
26,13430127
144
551
2^3 * 3 * 7 * 19 * 29
53089
31
28,209764919
156
553
2^5 * 3 * 7 * 79
224401
31
22,816399287
128
561
2^4 * 3 * 5^2 * 11 * 17
381481
31
22,816399287
128
561
2^3 * 3 * 5 * 11 * 17^2
99961
31
21,512605042
128
595
2^3 * 3 * 5 * 7^2 * 17
271489
31
28,28854314
200
707
2^7 * 3 * 7 * 101
256369
31
28,309305374
216
763
2^4 * 3 * 7^2 * 109
150721
31
26,496815287
208
785
2^6 * 3 * 5 * 157
447841
31
26,580921758
248
933
2^5 * 3^2 * 5 * 311
23209
31
33,298862461
322
967
2^3 * 3 * 967
39841
31
26,345381526
328
1245
2^5 * 3 * 5 * 83
421009
31
28,411811652
356
1253
2^4 * 3 * 7^2 * 179
389041
31
26,650215916
432
1621
2^4 * 3 * 5 * 1621
289511
31
34,485855411
768
2227
2 * 5 * 13 * 17 * 131
111409
31
30,159414046
700
2321
2^4 * 3 * 11 * 211
337681
31
22,515991471
528
2345
2^4 * 3^2 * 5 * 7 * 67
136751
31
39,926873857
1092
2735
2 * 5^3 * 547
326881
31
26,549192364
904
3405
2^5 * 3^2 * 5 * 227
342049
31
28,515296099
1016
3563
2^5 * 3 * 7 * 509
196081
31
24,675642595
1008
4085
2^4 * 3 * 5 * 19 * 43
276721
31
26,643538595
1536
5765
2^4 * 3 * 5 * 1153
61151
31
39,96729354
2444
6115
2 * 5^2 * 1223
135719
31
43,767223213
2700
6169
2 * 11 * 31 * 199
53881
31
26,607275427
1792
6735
2^3 * 3 * 5 * 449
175081
31
26,648389308
1944
7295
2^3 * 3 * 5 * 1459
207481
31
19,98843262
1728
8645
2^3 * 3 * 5 * 7 * 13 * 19
216841
31
24,438295517
2208
9035
2^3 * 3 * 5 * 13 * 139
296041
31
26,655857317
3288
12335
2^3 * 3 * 5 * 2467
307129
31
32,663905603
4180
12797
2^3 * 3 * 67 * 191
31391
31
38,534565148
6048
15695
2 * 5 * 43 * 73
169991
31
39,343490794
6688
16999
2 * 5 * 89 * 191
483289
31
30,749366837
6192
20137
2^3 * 3 * 13 * 1549
65831
31
38,450554458
12656
32915
2 * 5 * 29 * 227
290761
31
26,655661026
9688
36345
2^3 * 3 * 5 * 2423
88079
31
48,883943777
21528
44039
2 * 47 * 937
285757
31
33,331933538
23812
71439
2^2 * 3 * 23813
444463
31
33,332883351
24692
74077
2 * 3 * 74077
250799
31
49,999601273
62699
125399
2 * 125399
360007
31
32,16835275
57904
180003
2 * 3 * 29 * 2069
363359
31
47,054420159
85488
181679
2 * 17 * 10687
396871
31
26,664650893
52912
198435
2 * 3 * 5 * 13229
397799
31
49,999748616
99449
198899
2 * 198899
384913
30
30,303030303
10
33
2^4 * 3^7 * 11
133261
30
26,654660063
592
2221
2^2 * 3 * 5 * 2221
140071
30
21,109445277
704
3335
2 * 3 * 5 * 7 * 23 * 29
124153
30
28,532766286
1476
5173
2^3 * 3 * 7 * 739
209353
30
27,513470136
2400
8723
2^3 * 3 * 11 * 13 * 61
343381
30
25,944434737
7424
28615
2^2 * 3 * 5 * 59 * 97
87481
29
26,666666667
4
15
2^3 * 3^7 * 5
345601
29
26,666666667
4
15
2^9 * 3^3 * 5^2
193751
29
38,709677419
12
31
2 * 5^5 * 31
33601
29
22,857142857
8
35
2^6 * 3 * 5^2 * 7
47041
29
22,857142857
8
35
2^6 * 3 * 5 * 7^2
453601
29
22,857142857
8
35
2^5 * 3^4 * 5^2 * 7
33049
29
31,37254902
16
51
2^3 * 3^5 * 17
366001
29
26,229508197
16
61
2^4 * 3 * 5^3 * 61
336961
29
24,615384615
16
65
2^6 * 3^4 * 5 * 13
473089
29
25,974025974
20
77
2^11 * 3 * 7 * 11
406561
29
20,779220779
16
77
2^5 * 3 * 5 * 7 * 11^2
257401
29
22,377622378
32
143
2^3 * 3^2 * 5^2 * 11 * 13
463321
29
22,377622378
32
143
2^3 * 3^4 * 5 * 11 * 13
240769
29
28,708133971
60
209
2^7 * 3^2 * 11 * 19
451441
29
22,966507177
48
209
2^4 * 3^3 * 5 * 11 * 19
143263
29
28,496042216
108
379
2 * 3^3 * 7 * 379
305761
29
21,098901099
96
455
2^5 * 3 * 5 * 7^2 * 13
20231
29
32,268907563
192
595
2 * 5 * 7 * 17^2
47881
29
21,654135338
144
665
2^3 * 3^2 * 5 * 7 * 19
478801
29
21,654135338
144
665
2^4 * 3^2 * 5^2 * 7 * 19
312841
29
23,935558113
208
869
2^3 * 3^2 * 5 * 11 * 79
120121
29
19,180819181
192
1001
2^3 * 3 * 5 * 7 * 11 * 13
474769
29
28,38944495
312
1099
2^4 * 3^3 * 7 * 157
238681
29
23,167420814
256
1105
2^3 * 3^3 * 5 * 13 * 17
217561
29
22,239382239
288
1295
2^3 * 3 * 5 * 7^2 * 37
466201
29
22,239382239
288
1295
2^3 * 3^2 * 5^2 * 7 * 37
33289
29
31,146359048
432
1387
2^3 * 3 * 19 * 73
351121
29
19,68557758
288
1463
2^4 * 3 * 5 * 7 * 11 * 19
445537
29
24,822236587
384
1547
2^5 * 3^2 * 7 * 13 * 17
349801
29
23,785020011
416
1749
2^3 * 3 * 5^2 * 11 * 53
89041
29
22,425876011
416
1855
2^4 * 3 * 5 * 7 * 53
46489
29
30,562725865
592
1937
2^3 * 3 * 13 * 149
159769
29
28,481297882
632
2219
2^3 * 3^2 * 7 * 317
435649
29
33,318642574
756
2269
2^6 * 3 * 2269
280921
29
26,655275523
624
2341
2^3 * 3 * 5 * 2341
448561
29
22,600321027
704
3115
2^4 * 3^2 * 5 * 7 * 89
64279
29
33,32399888
1190
3571
2 * 3^2 * 3571
61681
29
26,562905318
1024
3855
2^4 * 3 * 5 * 257
494761
29
20,955614844
864
4123
2^3 * 3 * 5 * 7 * 19 * 31
210961
29
26,575654152
1168
4395
2^4 * 3^2 * 5 * 293
397849
29
30,081840301
1360
4521
2^3 * 3 * 11^2 * 137
330409
29
30,68206581
1408
4589
2^3 * 3^2 * 13 * 353
110569
29
31,256783156
1440
4607
2^3 * 3 * 17 * 271
339049
29
31,25929072
1472
4709
2^3 * 3^2 * 17 * 277
130729
29
30,695795851
1672
5447
2^3 * 3 * 13 * 419
291751
29
26,598114824
1552
5835
2 * 3 * 5^3 * 389
431929
29
28,538089682
1712
5999
2^3 * 3^2 * 7 * 857
492409
29
28,54218453
1952
6839
2^3 * 3^2 * 7 * 977
15791
29
39,974667511
3156
7895
2 * 5 * 1579
255649
29
33,320816122
2662
7989
2^5 * 3 * 2663
393649
29
32,532617973
2668
8201
2^4 * 3 * 59 * 139
361321
29
26,657810251
2408
9033
2^3 * 3 * 5 * 3011
18191
29
37,295217152
3392
9095
2 * 5 * 17 * 107
231961
29
26,652871185
2576
9665
2^3 * 3 * 5 * 1933
76831
29
24,490433424
3136
12805
2 * 3 * 5 * 13 * 197
394729
29
33,331306621
5482
16447
2^3 * 3 * 16447
394969
29
28,559275688
4700
16457
2^3 * 3 * 7 * 2351
35279
29
48,30205794
8520
17639
2 * 31 * 569
38639
29
49,997411874
9659
19319
2 * 19319
468889
29
28,561191585
5580
19537
2^3 * 3 * 7 * 2791
448003
29
33,331994054
8296
24889
2 * 3^2 * 24889
290351
29
39,993111762
11612
29035
2 * 5^2 * 5807
481009
29
30,269766823
9100
30063
2^4 * 3 * 11 * 911
312311
29
39,998719221
12492
31231
2 * 5 * 31231
63839
29
49,061687396
15660
31919
2 * 59 * 541
427151
29
39,995317804
17084
42715
2 * 5^2 * 8543
87911
29
39,058127631
17168
43955
2 * 5 * 59 * 149
440831
29
36,912188372
16272
44083
2 * 5 * 13 * 3391
147671
29
39,997291258
29532
73835
2 * 5 * 14767
199559
29
49,50139809
49392
99779
2 * 113 * 883
217439
29
46,148327339
50172
108719
2 * 13 * 8363
249311
29
39,456098833
49184
124655
2 * 5 * 107 * 233
270791
29
36,90535101
49968
135395
2 * 5 * 13 * 2083
322559
29
45,912983091
74048
161279
2 * 17 * 53 * 179
369071
29
34,543040616
63744
184535
2 * 5 * 13 * 17 * 167
375359
29
49,137090458
92220
187679
2 * 59 * 3181
425519
29
49,633623019
105600
212759
2 * 151 * 1409
465071
29
39,999139914
93012
232535
2 * 5 * 46507
470279
29
49,380153866
116112
235139
2 * 83 * 2833
479639
29
47,05548768
112848
239819
2 * 17 * 14107
491279
29
49,999796449
122819
245639
2 * 245639
151009
28
27,972027972
40
143
2^5 * 3 * 11^2 * 13
191161
28
26,214689266
232
885
2^3 * 3^4 * 5 * 59
298681
28
25,070309361
624
2489
2^3 * 3 * 5 * 19 * 131
140351
28
34,200213751
960
2807
2 * 5^2 * 7 * 401
133321
28
24,00240024
800
3333
2^3 * 3 * 5 * 11 * 101
282481
28
24,01585953
848
3531
2^4 * 3 * 5 * 11 * 107
344161
28
26,555090656
952
3585
2^5 * 3^2 * 5 * 239
485161
28
24,536235469
992
4043
2^3 * 3 * 5 * 13 * 311
224041
28
26,652383503
2488
9335
2^3 * 3 * 5 * 1867
160081
28
24,627686157
2464
10005
2^4 * 3 * 5 * 23 * 29
277747
28
26,821628394
12416
46291
2 * 3 * 7 * 17 * 389
174241
26
24,242424242
8
33
2^5 * 3^2 * 5 * 11^2
370441
26
22,857142857
8
35
2^3 * 3^3 * 5 * 7^3
149689
26
25,974025974
20
77
2^3 * 3^5 * 7 * 11
99289
26
28,426395939
56
197
2^3 * 3^2 * 7 * 197
275881
26
22,966507177
48
209
2^3 * 3 * 5 * 11^2 * 19
206641
26
22,299651568
64
287
2^4 * 3^2 * 5 * 7 * 41
204601
26
23,460410557
80
341
2^3 * 3 * 5^2 * 11 * 31
162649
26
33,200531208
250
753
2^3 * 3^4 * 251
104281
26
23,935558113
208
869
2^3 * 3 * 5 * 11 * 79
132049
26
28,353326063
260
917
2^4 * 3^2 * 7 * 131
333451
26
23,319838057
288
1235
2 * 3^3 * 5^2 * 13 * 19
437809
26
28,549501151
372
1303
2^4 * 3 * 7 * 1303
157081
26
19,556913675
256
1309
2^3 * 3 * 5 * 7 * 11 * 17
401101
26
22,737471952
304
1337
2^2 * 3 * 5^2 * 7 * 191
215161
26
24,093697713
432
1793
2^3 * 3 * 5 * 11 * 163
309289
26
28,462791961
524
1841
2^3 * 3 * 7^2 * 263
12391
26
22,469733656
464
2065
2 * 3 * 5 * 7 * 59
278881
26
22,581755594
656
2905
2^5 * 3 * 5 * 7 * 83
56611
26
24,419713831
768
3145
2 * 3^2 * 5 * 17 * 37
407401
26
22,621502209
768
3395
2^3 * 3 * 5^2 * 7 * 97
95929
26
28,521391043
1140
3997
2^3 * 3 * 7 * 571
163321
26
26,64707323
1088
4083
2^3 * 3 * 5 * 1361
422689
26
26,163979105
1152
4403
2^5 * 3 * 7 * 17 * 37
112249
26
33,311952106
1558
4677
2^3 * 3^2 * 1559
140281
26
22,720273738
1328
5845
2^3 * 3 * 5 * 7 * 167
250741
26
22,742282843
1584
6965
2^2 * 3^2 * 5 * 7 * 199
353329
26
31,300095096
2304
7361
2^4 * 3 * 17 * 433
92761
26
26,632169038
3088
11595
2^3 * 3 * 5 * 773
291481
26
22,791272128
2768
12145
2^3 * 3 * 5 * 7 * 347
385531
26
26,145825228
3360
12851
2 * 3 * 5 * 71 * 181
27191
26
39,985288709
5436
13595
2 * 5 * 2719
355609
26
30,235540258
4480
14817
2^3 * 3^2 * 11 * 449
244561
26
26,640497219
4072
15285
2^4 * 3 * 5 * 1019
451609
26
32,204921082
6060
18817
2^3 * 3 * 31 * 607
472921
26
22,816544024
4496
19705
2^3 * 3 * 5 * 7 * 563
425329
26
33,329571531
8860
26583
2^4 * 3 * 8861
228841
26
26,652683097
7624
28605
2^3 * 3 * 5 * 1907
57791
26
39,993078387
11556
28895
2 * 5 * 5779
302299
26
33,332671735
16794
50383
2 * 3 * 50383
187871
26
39,997870868
37572
93935
2 * 5 * 18787
209563
26
32,654775198
34216
104781
2 * 3 * 53 * 659
317831
26
38,873611679
61776
158915
2 * 5 * 37 * 859
439991
26
38,240869111
84128
219995
2 * 5 * 23 * 1913
459791
26
39,999130038
91956
229895
2 * 5 * 45979