Largest 10^147-c Brilliant Number (p74*p74)

[Alfred]

I'd like to continue with these numbers.
It will take a while.

[Alfred]

After a longer search, starting in September (!), I found this factorization:

10^199 - 5399 = 
16656894422236107849246117001467083363915297020262\
62362095233433137957466266604897548197173600787241 *
60035200719352030115130596816375251478500171431803\
22684010592432041391073140089147545414675783616961

Since c199 = 10^199 - 5399 is the largest 199-digit number with two 100-digit prime factors,
it is the 199-digit 2-brilliant number in base 10.

The attached file should help to check this assumption easily.
Any line in the file has two entries, the first is c, indicating the number,
the second is the smallest prime factor (of 10^199-c) or the letter 'p'.

[Alfred]

10^157 - 2049 is the largest 157-digit number with two 79-digit prime factors.

10^157 - 2049
1446814727739974723827555617027876206977909532017942734175294759323847644834853
6911735005366371832787385196708060058647586415356721193781047891582488320067667

The format of the attached "proving file" did not change.

[sweety439]

Originally Posted by Alfred

No 10^147-c with c>0 smaller than 28239 splits as p74*p74.

The attached file shows one factor (prime or composite but with less digits)
for any of these c's - or it indicates that 10^147-c is prime.

Since https://www.alpertron.com.ar/BRILLIANT.HTM is missing this number,
I hope it is new.

This site misses 154 digits.

MODERATOR CAUTION: Please stop posting inane "observations" like this. Like the next poster, and many other users, I am sick of them.

I am sure the people running projects like this know about the lacunae in their tables.

If you want to do something constructive about a missing entry, fill it in or at least do something to forward that aim. Otherwise, please hold your peace.

[Alfred]

Originally Posted by sweety439

This site misses 154 digits.

What is the worthy cause of this outstanding observation?

[swishzzz]

2^305-48019 = 6072848346102017942843738613347632788489697979 * 10733867787846864116326058114546589128269197047

Apparently someone had already found this factor as the entry shows up on factordb.com and was created some time before November 2018. A google search of either factor gives nothing.

Sieving of 10^199+c continues, with no even splits found so far for c < 16000.

[Alfred]

I'd like to take 10^201 - c.

[Alfred]

10^91 - 1250741
1130907742078987214643014936029
2064984395278432435681546498733
4282092540978287980470405630787

There is no larger 91-digit number which splits into three equally sized prime factors.

The attached file should prove this.

I omitted any line where 10^91-c is prime or where the smallest
prime factor (of 10^91-c) is smaller than 10^6.

PS: I'm still playing with 10^201-c.

[Alfred]

Originally Posted by Alfred

The attached file should prove this.

But it does not.
The file contains 282 lines, where the smallest primefactor has 31 digits.
For these numbers the attached file shows that the remaining cofactor is a 61-digit prime.

Now the proof should be complete.

I apologize the circumstances.

[Branger]

Originally Posted by swishzzz

Apparently someone had already found this factor as the entry shows up on factordb.com and was created some time before November 2018. A google search of either factor gives nothing.

I played around a bit with creating a python script to find base-2 brilliant numbers and found several, but all of them were previously reported to factordb.com. I'm starting to suspect that there are even more, though I'm not sure how to scrape the database to find them without adding a lot of unfactored composites to the database. Perhaps someone on this forum has more experience with that, and would be willing to have a look?

2^311-9397
=
62370919584932696459960851277070596883408884321
*
66887737222666271935456033050473264106633618731

2^311+69711
=
51666465841110031879560999958408509880659269639
*
80745791522933342211102055412622336041844745081

2^313-24133
=
100788170265999753017323085706257528483989089343
*
165569021385057306060482886322484491911556750213

2^313+8505
=
118458567629160086527486150975362030803169102833
*
140871184348377129067049239080578375237738238409

2^315-19015
=
216834485254286594903496585433315946327767764161
*
307836619227101788652208469732562326355490574073

2^315+42701
=
228669422455046776001485409864826671274859838381
*
291904331396343474258089280492317954768687954849

[swishzzz]

I have a Python web scraper that I use to check entries of the form n + c for varying c on factordb, though even filtering out composites which do not have a prime factor below 20M still generates about 3000 new factordb entries on a 100,000 search range for c. I suppose I can do some "light ecm" to further reduce that list by a factor of 5 or so, but it still takes a few hours to run a t25 on 3000+ 95-digit composites.

It would be nice if there was an easy way to find the smallest number that has been uploaded to factordb larger than a given number (as well as the largest number in factordb smaller than a given number), but I'm not sure how the numbers are stored internally in the database and doing such a query may be infeasible with the current infrastructure as there are over a billion entries in there already.