There’s a pattern here …

100000007003899576467 = 3.3.3.3.3.3.3.3.3.3.23.73630821715421
100000007003899576466 = 2.307 ...
100000007003899576465 = 5.67.298507483593730079
100000007003899576464 = 2.2.2.2.3.11.29.6143.121439.8754461
100000007003899576463 = 127.136649.5762220213481
100000007003899576462 = 2.7.7142857643135684033
100000007003899576461 = 3.33333335667966525487
100000007003899576460 = 2.2.5.101.191.223.1249.930567739
100000007003899576459 = 1031.6577.51769.284868053
100000007003899576458 = 2.3.3.5555555944661087581
100000007003899576457 = 13.17.19.41.47.6607.1870544887
100000007003899576456 = 2.2.2.3359.3721345899222223
100000007003899576455 = 3.5.7.7.8963.15179563906931
100000007003899576454 = 2.67957.158591.4639351721
100000007003899576453 = 11.9090909727627234223
100000007003899576452 = 2.2.3.107.96293.171203.4724207
100000007003899576451 =  ...
100000007003899576450 = 2.5.5.37.6833.7910735817349
100000007003899576449 = 3.3.673.16509824501221657
100000007003899576448 = 2.2.2.2.2.2.2.7.2447.45609787770329
100000007003899576447 = 4111.656603.37046713859
100000007003899576446 = 2.3.281.683.86840388249367
100000007003899576445 = 5.313.331.85931.2246507273
100000007003899576444 = 2.2.13.23.43 ...
100000007003899576443 = 3.89.30859.427001.28423531
100000007003899576442 = 2.11.4545454863813617111
100000007003899576441 = 7.14285715286271368063
100000007003899576440 = 2.2.2.3.3.3.5.17 ...
100000007003899576439 = 557.165037.1087836219871
100000007003899576438 = 2.19.149.5309.895469.3715069
100000007003899576437 = 3.31.1075268892515049209
100000007003899576436 = 2.2.797 ...
100000007003899576435 = 5.29.689655220716548803
100000007003899576434 = 2.3.7.79.30138639844454363
100000007003899576433 = 8369.11948859720862657
100000007003899576432 = 2.2.2.2.59.765949.138301911497
100000007003899576431 = 3.3.11.11.13.2003.6173.571283357
100000007003899576430 = 2.5.10000000700389957643
100000007003899576429 = 18133 ...
100000007003899576428 = 2.2.3.523.1181.13491716222263
100000007003899576427 = 7.353.45319.892990763323
100000007003899576426 = 2 ...
100000007003899576425 = 3.5.5.867253 ...
100000007003899576424 = 2.2.2.4751 ...
100000007003899576423 = 17.53.73.83.511963.35779619
100000007003899576422 = 2.3.3.941.5903885169671719
100000007003899576421 = 23.7537.576864321543571
100000007003899576420 = 2.2.5.7.11.71.167.269.3823.5325347
100000007003899576419 = 3.19.1754386087787711867
100000007003899576418 = 2.13.3846154115534599093
100000007003899576417 =  ...
100000007003899576416 = 2.2.2.2.2.3.41.25406505844486681
100000007003899576415 = 5 ...
100000007003899576414 = 2 ...
100000007003899576413 = 3.3.3.7.37.14300015301572941
100000007003899576412 = 2.2.103.106109.171469.13340281
100000007003899576411 = 100000007003899576411
100000007003899576410 = 2.3.5.47.61 ...
100000007003899576409 = 11.9203.987820246400873
100000007003899576408 = 2.2.2.97.251.4567.89021.1262819
100000007003899576407 = 3.139 ...
100000007003899576406 = 2.7.7.17.29.31.8311.29339.273821
100000007003899576405 = 5.13 ...
100000007003899576404 = 2.2.3.3.359.521 ...
100000007003899576403 = 163.389.977.10993.146842589
100000007003899576402 = 2 ...
100000007003899576401 = 3.43.775193852743407569
100000007003899576400 = 2.2.2.2.5.5.19.1607.8187862886377
100000007003899576399 = 7.14285715286271368057
100000007003899576398 = 2.3.11.23.67.263.647.5273.1095811
100000007003899576397 = 480941 ...
100000007003899576396 = 2.2.25000001750974894099
100000007003899576395 = 3.3.5.2222222377864435031
100000007003899576394 = 2.2347.21303793567085551
100000007003899576393 = 113.6637.133336720535453
100000007003899576392 = 2.2.2.3.7.13.5051.17791.509529893
100000007003899576391 = 131.211.999853.3618346267
100000007003899576390 = 2.5.199.50251259800954561
100000007003899576389 = 3.17.1960784451056854439
100000007003899576388 = 2.2.25000001750974894097
100000007003899576387 = 11.197.65899.700264797439
100000007003899576386 = 2.3.3.3.3 ...
100000007003899576385 = 5.7.2857143057254273611
100000007003899576384 = 2.2.2.2.2.2.25169.62080341270449
100000007003899576383 = 3.16889.1973671364081149
100000007003899576382 = 2.541.691.133750286899561
100000007003899576381 = 19.997.4271.35407.34908611
100000007003899576380 = 2.2.3.5.4327 ...
100000007003899576379 = 13.76379.100712345423077
100000007003899576378 = 2.7.5857.1219542025462811
100000007003899576377 = 3.3.29.8011.47826961588687
100000007003899576376 = 2.2.2.11.37.151.7219.41761.674669
100000007003899576375 = 5.5.5.23.23.31.41.109.10915969081
100000007003899576374 = 2.3.16666667833983262729

I just don’t know what it is.

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12 Comments

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12 responses to “There’s a pattern here …

  1. Jw

    That made me laugh so hard!

  2. No idea what either side means.

  3. salsaman123

    The numbers on the right are integer factors of the numbers on the left ?
    Looks like you found a prime number too.

    • rich

      Right .. of course. I wrote the program that made this.

      The question is .. what’s the pattern here? Doesn’t it look interesting. There are numbers made of lots of small primes. Then numbers which are (small prime x huge prime). Then the occasional prime.

      Gah, it’s annoying.

      • salsaman123

        If you *could* find a pattern then most likely you would win a Field Prize for maths, as you would have discovered a novel algorithm for finding primes. People waaaaay smarter than us have been trying this for millenia, and have not succeeded. The only obvious pattern is which numbers are *not* included (odd numbers will never include 2, only every third number will include 3, etc).

  4. I would say instead of looking at the numbers themselves, look to see how many primes make up a number. Is the pattern you are seeing there?

    • rich

      OK so the left column is a series of large numbers, and the right column is the integer factorization of each number into primes. So far so easy.

      The question is the amazing set of patterns (or otherwise??) this reveals on the right hand side.

      • rich

        The “…” is because the factorization function I wrote is very trivial and stupid, so it doesn’t find any factors over 1000000 unless the preceding division produced a prime (by Miller-Rabin primality testing).

  5. Michael

    Do you have a full dump of the sequence? I’m interested in the distribution of numbers that have comparatively large prime number factors compared to numbers that are composed of only small primes.

    I just finished getting my number theory cherry popped with a class project to break RSA. I got to 131 bit encryption on a quad core, but the Prof’s 196 bit key stopped me dead in my tracks. :(

    • rich

      I do, but my factorization function is too embarrassing to share with the general public. In any case it’s real easy to write something that dumps out these factors (at least for the small primes under ~1000000) using a library like GMP.

  6. DDD

    A fun thing to think about is what a computer would be like if instead of power of 2 binary, it used a prime factors decomposition to represent numbers.

    Easy to factor and multiply/divide. Hard to add and subtract ;)

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