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.

That made me laugh so hard!

No idea what either side means.

The numbers on the right are integer factors of the numbers on the left ?

Looks like you found a prime number too.

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.

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).

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?

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.

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).

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.ðŸ˜¦

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.

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 subtractðŸ˜‰

Tricky to convert a string to a number too …