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4-Brilliant results

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  • jim_fougeron
    These are minimal 4 brilliant numbers: 10^29+784329 P8 21977377 P8 13503449 P8 15690811 P8 21475043 10^30+46197 P8 24847783 P8 26380859 P8 37443787 P8 40742123
    Message 1 of 4 , Jun 2 9:38 AM
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      These are minimal 4 brilliant numbers:

      10^29+784329
      P8 21977377
      P8 13503449
      P8 15690811
      P8 21475043

      10^30+46197
      P8 24847783
      P8 26380859
      P8 37443787
      P8 40742123

      10^31+120531
      P8 40738811
      P8 56976001
      P8 52961729
      P8 81346249

      10^33+6379
      P9 169058819
      P9 132294061
      P9 121022911
      P9 369448771

      10^34+1167691
      P9 117930893
      P9 381975661
      P9 932958863
      P9 237943709

      10^35+1553517
      P9 229833959
      P9 871052447
      P9 837572501
      P9 596374529

      10^37+73269
      P10 2113986011
      P10 1015004657
      P10 2193454499
      P10 2124717653

      10^38+1505619
      P10 3280439369
      P10 3877244737
      P10 2535959857
      P10 3100290539

      10^39+5560879
      P10 5684681111
      P10 7330103057
      P10 2806287299
      P10 8551684723

      10^41+270387
      P11 41156248421
      P11 10057723799
      P11 16439060371
      P11 14695606843

      10^42+190281
      P11 12904941277
      P11 28529199667
      P11 52555058197
      P11 51682064947

      10^43+186541
      P11 94474714183
      P11 36717661187
      P11 40254606487
      P11 71613321583

      *** Other 4-Brilliants above minimum ***

      10^37+638689
      10^37+1382311
      10^37+1564533
      10^37+2791417

      10^38+1804257
      10^38+3412779
      10^38+3750189
      10^38+4302273
      10^38+4357653
      10^38+4664551

      10^39+5785819

      10^41+914677
      10^41+2152377
      10^41+2878939
      10^41+6319731

      10^42+2775327
      10^42+4837459
      10^42+6381183
      10^42+6557463
      10^42+7131499

      10^43+3949107
      10^43+4037007
      10^43+8226409
      10^43+12538639
      10^43+14803329
      10^43+15776599
      10^43+18181371
      10^43+19461057

      ** Others numbers with 4 factors (all at least minimum sized) **

      10^30+13249

      10^34+912769
      10^34+898473

      10^35+57877
      10^35+83283
      10^35+167851
      10^35+201313
      10^35+217953
      10^35+305071
      10^35+432159
      10^35+472191
      10^35+763197
      10^35+805059
      10^35+852223
      10^35+895101
      10^35+934269
      10^35+949519
      10^35+1122801
      10^35+1133499
      10^35+1141719
      10^35+1161231
      10^35+1297377
      10^35+1313523
      10^35+1325701
      10^35+1340301
      10^35+1441437
      10^35+1482309
      10^35+1564899
      10^35+1581937

      10^38+2689791
      10^38+3577717
      10^38+3767577
      10^38+1254333
      10^38+2539917

      10^39+333871
      10^39+758949
      10^39+764533
      10^39+1037721
      10^39+1415329
      10^39+1690609
      10^39+2034573
      10^39+2106597
      10^39+2592373
      10^39+2684733
      10^39+2770941
      10^39+2835777
      10^39+2909689
      10^39+3025983
      10^39+3066979
      10^39+3626913
      10^39+3807867
      10^39+3895363
      10^39+4280721
      10^39+4322001
      10^39+4427527
      10^39+4469689
      10^39+4787461
      10^39+4816581
      10^39+4820919
      10^39+5068873
      10^39+5150637
      10^39+5590233
      10^39+5805369
      10^39+5835429
      10^39+5909323
      10^39+5980249
      10^39+6391461
      10^39+6435531
      10^39+6913497
      10^39+6989853
      10^39+7102647
      10^39+7159801
      10^39+7236547
      10^39+7329013
      10^39+7340637
      10^39+7374271
      10^39+7728801
      10^39+7771251
      10^39+7817247
      10^39+7915591
      10^39+7960879
      10^39+8043423
      10^39+8124879
      10^39+8200117
      10^39+8258151
      10^39+8491621
      10^39+8626783
      10^39+8730189
      10^39+8835073
      10^39+9018277
      10^39+9147397
      10^39+9153423
      10^39+9168621
      10^39+9170949
      10^39+9185239
      10^39+9496363
      10^39+9599373

      10^42+1964359
      10^42+5635053
      10^42+5758111
      10^42+7236169
      10^42+8344723
      10^42+8953329

      10^43+83407
      10^43+319807
      10^43+329017
      10^43+488967
      10^43+519759
      10^43+690601
      10^43+713089
      10^43+961399
      10^43+1103359
      10^43+1180369
      10^43+1313221
      10^43+1581993
      10^43+1985653
      10^43+2419801
      10^43+2534997
      10^43+2568813
      10^43+3482869
      10^43+3599529
      10^43+3959937
      10^43+3961209
      10^43+4075683
      10^43+4104109
      10^43+4330891
      10^43+4499847
      10^43+4516347
      10^43+4749087
      10^43+5046609
      10^43+5278801
      10^43+5627137
      10^43+6106347
      10^43+6129481
      10^43+6173979
      10^43+6354609
      10^43+6460447
      10^43+6669907
      10^43+7395673
      10^43+7712119
      10^43+7881607
      10^43+8215371
      10^43+8733453
      10^43+8747793
      10^43+8794189
      10^43+8801691
      10^43+8987809
      10^43+9074149
      10^43+9092373
      10^43+9110337
      10^43+9113643
      10^43+9187837
      10^43+9348321
      10^43+9536571
      10^43+9627591
      10^43+9686059
      10^43+9763747
      10^43+9825541
      10^43+10528071
      10^43+10587187
      10^43+10612773
      10^43+11009983
      10^43+11013211
      10^43+11084163
      10^43+11101741
      10^43+11328603
      10^43+11367607
      10^43+11672499
      10^43+11699563
      10^43+12012253
      10^43+12219919
      10^43+12373629
      10^43+12391431
      10^43+12543193
      10^43+12664711
      10^43+12813871
      10^43+12907117
      10^43+13422387
      10^43+13610919
      10^43+13720647
      10^43+13974963
      10^43+13978743
      10^43+14009023
      10^43+14403219
      10^43+14484451
      10^43+14706189
      10^43+14842821
      10^43+14902243
      10^43+15322371
      10^43+16908873
      10^43+17529013
      10^43+17788737
      10^43+17972127
      10^43+18061531
      10^43+18193353
      10^43+18415033
      10^43+19028211
      10^43+19126147
      10^43+19221889
    • Phil Carmody
      ... [SNIP] Grand work, Jim! Do we yet have a heuristic for the delta from the power of ten for each of the brilliant types. It appears that with the increased
      Message 2 of 4 , Jun 2 11:44 AM
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        --- jim_fougeron <jfoug@...> wrote:
        > These are minimal 4 brilliant numbers:
        [SNIP]

        Grand work, Jim!

        Do we yet have a heuristic for the delta from the power of ten for
        each of the brilliant types. It appears that with the increased
        choice of primes, there's a limited growth of the delta, and
        sometimes it almost looks like it's hardly growing at all. However,
        any formal attack evades me. Probably the 2 factor type is the most
        attackable.

        Phil

        =====
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      • alpertron
        ... [snip] It appears that your computer worked a lot. Thanks a lot, Jim. I ve just uploaded you results to: http://www.alpertron.com.ar/BRILLIANT.HTM Best
        Message 3 of 4 , Jun 2 7:18 PM
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          --- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:
          > These are minimal 4 brilliant numbers:

          [snip]

          It appears that your computer worked a lot. Thanks a lot, Jim.

          I've just uploaded you results to:

          http://www.alpertron.com.ar/BRILLIANT.HTM

          Best regards,

          Dario Alejandro Alpern
          Buenos Aires - Argentina
          http://www.alpertron.com.ar/ENGLISH.HTM
        • jim_fougeron
          ... Actually no. I worked more than my computer (for the larger numbers at least). When starting out, I used this technique: (for 10^29+ and 10^30+) 1. trial
          Message 4 of 4 , Jun 3 5:13 AM
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            --- In primenumbers@y..., "alpertron" <alpertron@h...> wrote:
            >--- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:
            >> These are minimal 4 brilliant numbers:
            >
            >[snip]
            >
            >It appears that your computer worked a lot. Thanks a lot, Jim.

            Actually no. I worked more than my computer (for the larger numbers
            at least).

            When starting out, I used this technique: (for 10^29+ and 10^30+)
            1. trial factor a 5000000 range with CPAPSieve up to prime 10000000
            2. compute ceil((10^29)^.25) (17782795)
            3. trial factor the values left over up to this point.
            4. Whatever items factored out on step 2 (not too many) are the only
            candidates which can be brilliant-4.
            5. Check each of these by fully factoring until a brilliant was found
            6. For 10^30+ step 2 is ceil((10^30)^.25) which is 31622776

            For the larger numbers (where I show a lot of additional brilliants,
            and "large enough" 4 factor results), I used this method: (10^35+)

            1. trial factor a 5000000 range with CPAPSieve up to prime 100000000
            2. modified CPAPSieve to not eliminate candidates, but to count how
            many factors each had seen. Then simply run it to prime 1000000000
            and output all candidates which 4 factors were found.

            Method 2 is a constant time method, however, each time you increase
            the size of the brilliant factors by 1 digit, this method take 10
            times as long to complete.

            Using something like the method 2 would quickly these brilliants while
            the size of the factors are small.

            Jim.

            >I've just uploaded you results to:
            >
            >http://www.alpertron.com.ar/BRILLIANT.HTM
            >
            >Best regards,
            >
            >Dario Alejandro Alpern
            >Buenos Aires - Argentina
            >http://www.alpertron.com.ar/ENGLISH.HTM
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