mersenneforum.org Smallest 10^179+c Brilliant Number (p90 * p90)
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 2019-09-09, 01:32 #1 2147483647   Dec 2016 100102 Posts Smallest 10^179+c Brilliant Number (p90 * p90) Brilliant numbers are semiprimes where both prime factors have the same number of digits. According to this table, the smallest n such that the smallest n digit brilliant number is unknown is n=146. For the past ~2.5 weeks I've being doing a bunch of SNFS and I just found it: 10^145 + 26019 = 1712231579162695023146424005134362656947458223008859385200062175608237361 * 5840331484185181666946526399283426386742617220393273278243146252757154579 I've actually sieved all the unfactored numbers out to c = ~38k but fell behind on the postprocessing until yesterday. Took ~150 SNFS runs to find I think, although ~20 of those were with c > 26019 because c = 26019 and a few others got missed for a while because they were undersieved. I found a few near-misses for c < 26019. There was a p72 * p74 at c = 8599 (and another at c = 32973), and a few p71 * p75s too.
 2019-09-09, 01:56 #2 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·7·11·13 Posts Forgive my ignorance, but why would it be considered unknown? There are plenty of known 73 dd prime numbers that are very likely to result in a 146 dd semiprime: http://factordb.com/listtype.php?t=4...ge=100&start=0 What am I misunderstanding here? Thanks in advance.
2019-09-09, 02:37   #3
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

2·5·11·43 Posts

Quote:
 Originally Posted by a1call Forgive my ignorance, but why would it be considered unknown?
Ponder the meaning of "smallest" in "smallest brilliant number of n digits."

 2019-09-09, 02:56 #4 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×7×11×13 Posts Acknowledged, Thank you very much.
 2019-09-09, 03:17 #5 rudy235     Jun 2015 Vallejo, CA/. 24·61 Posts I would clarify further and call it "smallest possible".
 2019-09-09, 08:09 #6 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 585310 Posts Can I suggest looking at the factorization factory if you want to do more of these. A lot of the work can be shared between numbers. I would think that a degree 2 or 3 poly with a common rational poly would make sense here.
2019-09-09, 09:04   #7
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

11×967 Posts

Quote:
 Originally Posted by 2147483647 Brilliant numbers are semiprimes where both prime factors have the same number of digits. According to this table, the smallest n such that the smallest n digit brilliant number is unknown is n=146. For the past ~2.5 weeks I've being doing a bunch of SNFS and I just found it: 10^145 + 26019 = 1712231579162695023146424005134362656947458223008859385200062175608237361 * 5840331484185181666946526399283426386742617220393273278243146252757154579
Congratulations.

It's about time I set the upper limit again.

Paul

 2019-09-11, 22:19 #8 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 638310 Posts Well, that was indecently lucky ... 10^179+1039 = Code: p90 factor: 140837725563903108928160798541416779343987069101706278981482452086290437833772503658895889 p90 factor: 710037027363285744751511636041030962532956891436161203659956860276022774234895368099896351 10^179+n for n<1039 is either prime, or divisible by a prime <2^23, or divisible by a prime in the list below Code: 19 14101387 49 14147552822097691663 57 35782408050786092825897707 103 3108967483 109 383943298877 141 706598062641397 231 1451243290927197419514136787 237 2500422969821983 253 106469781304792106087 301 974764229 333 900576964916303 369 10571453393 391 10206877 469 17093751491 481 29314808171939 487 99321412503984693433 559 70893363894244915493 627 96071164333023421 631 1677873931457 657 8969231 757 735502689743 769 11193310726676637973 811 69672262968268248649729 823 1144280823821 829 8505508806737 879 37531709701 889 794674405363 901 22545947828834902287109968139 937 420490046629 993 57163357 1033 3191058343795684819 A few core-months of ECM, and this was the second SNFS job (about 700k thread-seconds sieving) Last fiddled with by fivemack on 2019-09-11 at 22:24
2019-09-17, 06:30   #9
lavalamp

Oct 2007
Manchester, UK

24778 Posts

Quote:
 Originally Posted by rudy235 I would clarify further and call it "smallest possible".
Do you think that merely calling it the smallest would leave open the possibility of finding a smallester one?

2019-09-17, 06:33   #10
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

2×5×11×43 Posts

Quote:
 Originally Posted by lavalamp Do you think that merely calling it the smallest would leave open the possibility of finding a smallester one?
smallest possible versus smallest known. In other contexts, a useful distinction.

2019-09-17, 07:20   #11
rudy235

Jun 2015
Vallejo, CA/.

24·61 Posts

Quote:
 Originally Posted by VBCurtis smallest possible versus smallest known. In other contexts, a useful distinction.
Yes.

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