This README goes with fastprimes5.cc
====================================
____ offset relative to previous candidate.
| _ candidates (non-primes are put between parenthesis).
| |
v v
+0 1
----┼---
p_ =|1¹(0)
| { +1 } +1 +1 +1 +1 +1 +1 ... a series of ones, repeated.
| 1 2 3 4 5 6 7 8 ... all integers, starting at 1²
| ^ ^------------.
window2_:{start_:1², head_:1, last_:2},
window1_:{start_:1¹, head_:1, last_:1²}
| ↓ { +1 } +1 +1 +1 +1 +1 +1 ... the differences between:
v 1¹ = 1¹ 2 3 4 5 6 7 8 ... all integers, starting at 1¹
1 | <-- last_candidate_
+1 2 | .------------------------ expected_failure_:2
+1 3 | |
+1 (4) = 2² | | <-- next_prime_squared_:4
----┼--- | v
p_ =|2¹(1) `--------> 2 3 4 5 6 7 8 ... all integers, starting at 1¹
| 2 2 2 2 2 2 2 ... expected_failure_ never matches and therefore never changes
| 4 5 6 7 8 9 10 11 ... all integers, starting at 2² <------.
| { +1 } +1 +1 +1 +1 +1 +1 ... the differences between: |
| 4 5 6 7 8 9 10 11 ... the ones left after removing the 'multiplied by 1¹' from .'
| ↑ ^------------.
window2_:{start_:2², head_:4, last_:5},
window1_:{start_:2¹, head_:2, last_:2²}
| ↓ { +1 } +1 +1 +1 +1 +1 +1 ... the differences between:
v 2¹ = 2¹ 3 4 5 6 7 8 9 ... all integers, starting at 2¹
4 | <-- last_candidate_:4
+1 5 |
+1 (6) = 2¹ * 3 <-- expected_failure_:6
+1 7 |
+1 (8) = 2¹ * 4 <-- expected_failure_:8
+1 (9) = 3² | <-- next_prime_squared_:9
----┼--- |
p_ =|3¹(2) `--------> 5 6 7 8 ... all integers, starting at 2¹
| 10 12 14 16 ... multiplied by 2¹ (this is what expected_failure_ runs over), remove these from:
| 9 10 11 12 13 14 15 16 ... all integers, starting at 3²
| { +2 } +2 +2 ... the differences between:
| 9 11 13 15 ... the ones left after skipping expected_failure_'s.
| ↑ ^----------.
window2_:{start_:3², head_:9, last_:11}
window1_:{start_:3¹, head_:3, last_:3²}
| ↓ { +2 } +2 +2 +2 +2 +2 +2 ... the differences between:
v 3¹ = 3¹ 5 7 9 11 13 15 17 ... all integers not divisible by primes less than 3¹
9 | <-- last_candidate_:9
+2 11 |
+2 13 |
+2 (15) = 3¹ * 5 <-- expected_failure_:15
+2 17 |
+2 19 |
+2 (21) = 3¹ * 7 <-- expected_failure_:21
+2 23 |
+2 (25) = 5² | <-- next_prime_squared_:25
----┼---- |
p_ =|5¹(3) `-------> 9 11 13 ... all integers not divisible by primes less than 3¹
| 27 33 39 ... multiplied by 3¹ (this is what expected_failure_ runs over), remove these from:
| 25 27 29 31 33 35 37 39 ... all integers, starting at 5², not divisible by primes less than 3¹
| { +4 +2 } +4 +2 ... the differences between:
| 25 29 31 35 37 ... the ones left after skipping expected_failure_'s.
| ↑ ^-----------.
window2_:{start_:5², head_:25, last_:29}
window1_:{start_:5¹, head_:5, last_:5²}
| ↓ { +2 +4 } +2 +4 +2 +4 +2 ... the differences between:
v 5¹ = 5¹ 7 11 13 17 19 23 25 ... all integers not divisible by primes less than 5¹
25 | <-- last_candidate_:25
+4 29 |
+2 31 |
+4 (35) = 5¹ * 7 <-- expected_failure_:35
+2 37 |
+4 41 |
+2 43 |
+4 47 |
+2 (49) = 7^2 | <-- next_prime_squared_:49
----┼---- |
p_ =|7¹(4) `---------> 11 13 17 19 23 25 ... all integers not divisible by primes less than 5¹
| 55 65 85 95 115 125 ... multiplied by 5¹ (this is what expected_failure_ runs over), remove these from:
| 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103 107 109 113 115 119 121 125 127 ... all integers, starting at 7², not divisible by primes less than 5¹
| { +4 +6 +2 +6 +4 +2 +4 +2 } +4 +6 +2 +6 +4 +2 +4 +2 +4 +6 +2 +6 ... the differences between:
| 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 ... the ones left after skipping expected_failure_'s.
| ↑ ^--------------.
window2_:{start_:7², head_:49, last_:53}
window1_:{start_:7¹, head_:7, last_:7²}
| ↓ { +4 +2 +4 +2 +4 +6 +2 +6 } +4 +2 +4 +2 ... the differences between:
v 7¹ = 7¹ 11 13 17 19 23 29 31 37 41 43 47 49 ... all integers not divisible by primes less than 7¹
49 | <-- last_candidate_:49
+4 53 |
+6 59 |
+2 61 |
+6 67 |
+4 71 |
+2 73 |
+4 (77) = 7 * 11 <-- expected_failure_:77
+2 79 |
+4 83 |
+6 89 |
+2 (91) = 7 * 13 <-- expected_failure_:91
+6 97 |
+4 101 |
+2 103 |
+4 107 |
+2 109 |
+4 113 |
+6 (119) = 7 * 17 <-- expected_failure_:119
+2 (121) = 11^2 | <-- next_prime_squared_:121
----┼---- |
p_ =|11¹(5) `--------------> 19 23 29 31 ... all integers not divisible by primes less than 7¹
| 133 161 203 217 ... multiplied by 7¹ (this is what expected_failure_ runs over), remove these from:
| 121 127 131 133 137 139 143 149 151 157 161 163 167 169 173 179 181 187 191 193 197 199 203 209 211 217 221 ...
| 6 4 2+ 4 2 4 6 2 6 4+ 2 4 2 4 6 2 6 4 2 4 2 4+ 6 2 6+ 4 ...
v { +6 +4 +6 +2 +4 +6 +2 +6 +6 +4 +2 +4 +6 +2 +6 +4 +2 +4 +2 +10 +2 +10 ...
121
+6 127
+4 131
+6 137
+2 139
+4 (143) = 11 * 13
+6 149 |
+2 151 |
+6 157 |
+6 163 |
+4 167 |
+2 (169) = 13^2 |
|
`--------+4-------> 17 -------+2------> 19 ----+4---> 23 -----+6-----> 29 -+2-> 31 ... (not div by 2,3,5,7)
+4 173 ---------------> 173 179 181 187 191 193 197 199 209 211 221 ...
4 6 2 6+ 4 2 4 2 10+ 2 10 ...
-------- { +4 +6 + 2 +10 +2 +4 +2 +12 +10 +2 +4 +2 +4 +6 +2 +6 +4 +6 +6 +6 +2 +6 +4 +2 +6 ...
+4 173
+6 179
+2 181
+10 191
+2 193
+4 197
+2 199
+12 211
+10 (221) = 13 * 17
+2 223
+4 227
+2 229
+4 233
+6 239
+2 241
+6 (247) = 13 * 19
+4 251
+6 257
+6 263
+6 269
+2 271
+6 277
+4 281
+2 283
+6 (289) = 17^2
--------
+4 293
+14 307
+4 311
+2 313
+4 317
+6 (323) = 17 * 19
+8 331
+6 337
+10 347
+2 349
+4 353
+6 359
+2 (361) = 19^2
--------
+6 367
+6 373
+6 379
+4 383
+6 389
+8 397
+4 401
+8 409
+10 419
+2 421
+10 431
+2 433
+4 (437) = 19 * 23
+2 439
+4 443
+6 449
+8 457
+4 461
+2 463
+4 467
+12 479
+8 487
+4 491
+8 499
+4 503
+6 509
+12 521
+2 523
+6 (529) = 23^2
--------
+12 541
+6 547
+10 557
+6 563
+6 569
+2 571
+6 577
+10 587
+6 593
+6 599
+2 601
+6 607
+6 613
+4 617
+2 619
+12 631
+10 641
+2 643
+4 647
+6 653
+6 659
+2 661
+6 (667) = 23 * 29
+6 673
+4 677
+6 683
+8 691
+10 701
+8 709
+4 (713) = 23 * 31
+6 719
+8 727
+6 733
+6 739
+4 743
+8 751
+6 757
+4 761
+8 769
+4 773
+14 787
+10 797
+12 809
+2 811
+10 821
+2 823
+4 827
+2 829
+10 839
+2 (841) = 29^2
--------
+12 853
+4 857
+2 859
+4 863
+14 877
+4 881
+2 883
+4 887
+12 (899) = 29 * 31
+8 907
+4 911
+8 919
+10 929
+8 937
+4 941
+6 947
+6 953
+8 (961) = 31^2
--------
+6 967
+4 971
+6 977
+6 983
+8 991
+6 997
+12 1009
+4 1013
+6 1019
+2 1021
+10 1031
+2 1033
+6 1039
+10 1049
+2 1051
+10 1061
+2 1063
+6 1069
+18 1087
+4 1091
+2 1093
+4 1097
+6 1103
+6 1109
+8 1117
+6 1123
+6 1129
+18 (1147) = 31 * 37
+4 1151
+2 1153
+10 1163
+8 1171
+10 1181
+6 1187
+6 1193
+8 1201
+12 1213
+4 1217
+6 1223
+6 1229
+2 1231
+6 1237
+12 1249
+10 1259
+12 (1271) = 31 * 41
+6 1277
+2 1279
+4 1283
+6 1289
+2 1291
+6 1297
+4 1301
+2 1303
+4 1307
+12 1319
+2 1321
+6 1327
+6 (1333) = 31 * 43
+28 1361
+6 1367
+2 (1369) = 37^2
--------
+4 1373
+8 1381
+18 1399
+10 1409
+14 1423
+4 1427
+2 1429
+4 1433
+6 1439
+8 1447
+4 1451
+2 1453
+6 1459
+12 1471
+10 1481
+2 1483
+4 1487
+2 1489
+4 1493
+6 1499
+12 1511
+6 (1517) = 37 * 41
+6 1523
+8 1531
+12 1543
+6 1549
+4 1553
+6 1559
+8 1567
+4 1571
+8 1579
+4 1583
+8 (1591) = 37 * 43
+6 1597
+4 1601
+6 1607
+2 1609
+4 1613
+6 1619
+2 1621
+6 1627
+10 1637
+20 1657
+6 1663
+4 1667
+2 1669
+12 (1681) = 41^2
--------
+12 1693
+4 1697
+2 1699
+10 1709
+12 1721
+2 1723
+10 1733
+8 1741
+6 1747
+6 1753
+6 1759
+4 (1763) = 41 * 43
+14 1777
+6 1783
+4 1787
+2 1789
+12 1801
+10 1811
+12 1823
+8 1831
+16 1847
+2 (1849) = 43^2
--------
+12 1861
+6 1867
+4 1871
+2 1873
+4 1877
+2 1879
+10 1889
+12 1901
+6 1907
+6 1913
+18 1931
+2 1933
+16 1949
+2 1951
+22 1973
+6 1979
+8 1987
+6 1993
+4 1997
+2 1999
+4 2003
+8 2011
+6 2017
+4 (2021) = 43 * 47
+6 2027
+2 2029
+10 2039
+14 2053
+10 2063
+6 2069
+12 2081
+2 2083
+4 2087
+2 2089
+10 2099
+12 2111
+2 2113
+16 2129
+2 2131
+6 2137
+4 2141
+2 2143
+10 2153
+8 2161
+18 2179
+24 2203
+4 2207
+2 (2209) = 47^2
--------
+4 2213
+8 2221
+16 2237
+2 2239
+4 2243
+8 2251
+16 2267
+2 2269
+4 2273
+8 2281
+6 2287
+6 2293
+4 2297
+12 2309
+2 2311
+22 2333
+6 2339
+2 2341
+6 2347
+4 2351
+6 2357
+14 2371
+6 2377
+4 2381
+2 2383
+6 2389
+4 2393
+6 2399
+12 2411
+6 2417
+6 2423
+14 2437
+4 2441
+6 2447
+12 2459
+8 2467
+6 2473
+4 2477
+14 (2491) = 47 * 53
+12 2503
+18 2521
+10 2531
+8 2539
+4 2543
+6 2549
+2 2551
+6 2557
+22 2579
+12 2591
+2 2593
+16 2609
+8 2617
+4 2621
+12 2633
+14 2647
+10 2657
+2 2659
+4 2663
+8 2671
+6 2677
+6 2683
+4 2687
+2 2689
+4 2693
+6 2699
+8 2707
+4 2711
+2 2713
+6 2719
+10 2729
+2 2731
+10 2741
+8 2749
+4 2753
+14 2767
+6 (2773) = 47 * 59
+4 2777
+12 2789
+2 2791
+6 2797
+4 2801
+2 2803
+6 (2809) = 53^2
--------
+10 2819
+14 2833
+4 2837
+6 2843
+8 2851
+6 2857
+4 2861
+18 2879
+8 2887
+10 2897
+6 2903
+6 2909
+8 2917
+10 2927
+12 2939
+14 2953
+4 2957
+6 2963
+6 2969
+2 2971
+28 2999
+2 3001
+10 3011
+8 3019
+4 3023
+14 3037
+4 3041
+8 3049
+12 3061
+6 3067
+12 3079
+4 3083
+6 3089
+20 3109
+10 3119
+2 3121
+6 (3127) = 53 * 59
+10 3137
+26 3163
+4 3167
+2 3169
+12 3181
+6 3187
+4 3191
+12 3203
+6 3209
+8 3217
+4 3221
+8 3229
+4 (3233) = 53 * 61
+18 3251
+2 3253
+4 3257
+2 3259
+12 3271
+28 3299
+2 3301
+6 3307
+6 3313
+6 3319
+4 3323
+6 3329
+2 3331
+12 3343
+4 3347
+12 3359
+2 3361
+10 3371
+2 3373
+16 3389
+2 3391
+16 3407
+6 3413
+20 3433
+16 3449
+8 3457
+4 3461
+2 3463
+4 3467
+2 3469
+12 (3481) = 59^2
--------
+10 3491
+8 3499
+12 3511
+6 3517
+10 3527
+2 3529
+4 3533
+6 3539
+2 3541
+6 3547
+10 3557
+2 3559
+12 3571
+10 3581
+2 3583
+10 3593
+6 (3599) = 59 * 61
+8 3607
+6 3613
+4 3617
+6 3623
+8 3631
+6 3637
+6 3643
+16 3659
+12 3671
+2 3673
+4 3677
+14 3691
+6 3697
+4 3701
+8 3709
+10 3719
+2 (3721) = 61^2
--------
+6 3727
+6 3733
+6 3739
+22 3761
+6 3767
+2 3769
+10 3779
+14 3793
+4 3797
+6 3803
+18 3821
+2 3823
+10 3833
+14 3847
+4 3851
+2 3853
+10 3863
+14 3877
+4 3881
+8 3889
+18 3907
+4 3911
+6 3917
+2 3919
+4 3923
+6 3929
+2 3931
+12 3943
+4 3947
+20 3967
+22 3989
+12 4001
+2 4003
+4 4007
+6 4013
+6 4019
+2 4021
+6 4027
+22 4049
+2 4051
+6 4057
+16 4073
+6 4079
+8 (4087) = 61 * 67
+4 4091
+2 4093
+6 4099
+12 4111
+16 4127
+2 4129
+4 4133
+6 4139
+14 4153
+4 4157
+2 4159
+18 4177
+24 4201
+10 4211
+6 4217
+2 4219
+10 4229
+2 4231
+10 4241
+2 4243
+10 4253
+6 4259
+2 4261
+10 4271
+2 4273
+10 4283
+6 4289
+8 4297
+30 4327
+4 (4331) = 61 * 71
+6 4337
+2 4339
+10 4349
+8 4357
+6 4363
+10 4373
+18 4391
+6 4397
+12 4409
+12 4421
+2 4423
+18 4441
+6 4447
+4 4451
+2 (4453) = 61 * 73
+4 4457
+6 4463
+18 4481
+2 4483
+6 (4489) = 67^2
--------
+4 4493
+14 4507
+6 4513
+4 4517
+2 4519
+4 4523
+24 4547
+2 4549
+12 4561
+6 4567
+16 4583
+8 4591
+6 4597
+6 4603
+18 4621
+16 4637
+2 4639
+4 4643
+6 4649
+2 4651
+6 4657
+6 4663
+10 4673
+6 4679
+12 4691
+12 4703
+18 4721
+2 4723
+6 4729
+4 4733
+18 4751
+6 (4757) = 67 * 71
+2 4759
+24 4783
+4 4787
+2 4789
+4 4793
+6 4799
+2 4801
+12 4813
+4 4817
+14 4831
+30 4861
+10 4871
+6 4877
+12 4889
+2 (4891) = 67 * 73
+12 4903
+6 4909
+10 4919
+12 4931
+2 4933
+4 4937
+6 4943
+8 4951
+6 4957
+10 4967
+2 4969
+4 4973
+14 4987
+6 4993
+6 4999
+4 5003
+6 5009
+2 5011
+10 5021
+2 5023
+16 5039
+2 (5041) = 71^2
--------
+10 5051
+8 5059
+18 5077
+4 5081
+6 5087
+12 5099
+2 5101
+6 5107
+6 5113
+6 5119
+28 5147
+6 5153
+14 5167
+4 5171
+8 5179
+4 (5183) = 71 * 73
+6 5189
+8 5197
+12 5209
+18 5227
+4 5231
+2 5233
+4 5237
+24 5261
+12 5273
+6 5279
+2 5281
+16 5297
+6 5303
+6 5309
+14 5323
+6 (5329) = 73^2
--------
+4 5333
+14 5347
+4 5351
+30 5381
+6 5387
+6 5393
+6 5399
+8 5407
+6 5413
+4 5417
+2 5419
+12 5431
+6 5437
+4 5441
+2 5443
+6 5449
+22 5471
+6 5477
+2 5479
+4 5483
+18 5501
+2 5503
+4 5507
+12 5519
+2 5521
+6 5527
+4 5531
+26 5557
+6 5563
+6 5569
+4 5573
+8 5581
+10 5591
+32 5623
+16 5639
+2 5641
+6 5647
+4 5651
+2 5653
+4 5657
+2 5659
+10 5669
+14 5683
+6 5689
+4 5693
+8 5701
+10 5711
+6 5717
+20 5737
+4 5741
+2 5743
+6 5749
+18 (5767) = 73 * 79
+12 5779
+4 5783
+8 5791
+10 5801
+6 5807
+6 5813
+8 5821
+6 5827
+12 5839
+4 5843
+6 5849
+2 5851
+6 5857
+4 5861
+6 5867
+2 5869
+10 5879
+2 5881
+16 5897
+6 5903
+20 5923
+4 5927
+12 5939
+14 5953
+28 5981
+6 5987
+20 6007
+4 6011
+18 6029
+8 6037
+6 6043
+4 6047
+6 6053
+6 (6059) = 73 * 83
+8 6067
+6 6073
+6 6079
+10 6089
+2 6091
+10 6101
+12 6113
+8 6121
+10 6131
+2 6133
+10 6143
+8 6151
+12 6163
+10 6173
+24 6197
+2 6199
+4 6203
+8 6211
+6 6217
+4 6221
+8 6229
+12 (6241) = 79^2
--------
+6 6247
+10 6257
+6 6263
+6 6269
+2 6271
+6 6277
+10 6287
+12 6299
+2 6301
+10 6311
+6 6317
+6 6323
+6 6329
+8 6337
+6 6343
+10 6353
+6 6359
+2 6361
+6 6367
+6 6373
+6 6379
+10 6389
+8 6397
+24 6421
+6 6427
+22 6449
+2 6451
+18 6469
+4 6473
+8 6481
+10 6491
+30 6521
+8 6529
+18 6547
+4 6551
+2 6553
+4 (6557) = 79 * 83
+6 6563
+6 6569
+2 6571
+6 6577
+4 6581
+18 6599
+8 6607
+12 6619
+18 6637
+16 6653
+6 6659
+2 6661
+12 6673
+6 6679
+10 6689
+2 6691
+10 6701
+2 6703
+6 6709
+10 6719
+14 6733
+4 6737
+24 6761
+2 6763
+16 6779
+2 6781
+10 6791
+2 6793
+10 6803
+20 6823
+4 6827
+2 6829
+4 6833
+8 6841
+16 6857
+6 6863
+6 6869
+2 6871
+12 6883
+6 (6889) = 83^2
--------
+10 6899
+8 6907
+4 6911
+6 6917
+30 6947
+2 6949
+10 6959
+2 6961
+6 6967
+4 6971
+6 6977
+6 6983
+8 6991
+6 6997
+4 7001
+12 7013
+6 7019
+8 7027
+12 7039
+4 7043
+14 7057
+12 7069
+10 7079
+24 7103
+6 7109
+12 7121
+6 7127
+2 7129
+22 7151
+8 7159
+18 7177
+10 7187
+6 7193
+14 7207
+4 7211
+2 7213
+6 7219
+10 7229
+8 7237
+6 7243
+4 7247
+6 7253
+30 7283
+14 7297
+10 7307
+2 7309
+12 7321
+10 7331
+2 7333
+16 7349
+2 7351
+18 7369
+18 (7387) = 83 * 89
+6 7393
+18 7411
+6 7417
+16 7433
+18 7451
+6 7457
+2 7459
+18 7477
+4 7481
+6 7487
+2 7489
+10 7499
+8 7507
+10 7517
+6 7523
+6 7529
+8 7537
+4 7541
+6 7547
+2 7549
+10 7559
+2 7561
+12 7573
+4 7577
+6 7583
+6 7589
+2 7591
+12 7603
+4 7607
+14 7621
+18 7639
+4 7643
+6 7649
+20 7669
+4 7673
+8 7681
+6 7687
+4 7691
+8 7699
+4 7703
+14 7717
+6 7723
+4 7727
+14 7741
+12 7753
+4 7757
+2 7759
+30 7789
+4 7793
+24 7817
+6 7823
+6 7829
+12 7841
+12 7853
+14 7867
+6 7873
+4 7877
+2 7879
+4 7883
+18 7901
+6 7907
+12 7919
+2 (7921) = 89^2
--------
The 1000-th prime is 7919