I made up some parameters and ran this C103 as a quartic SNFS job on CADO. Took a 2-hyperthreaded instance about 6 minutes to solve on a 12-core machine with 18 other threads busy.

And six more base-2 brilliant number, one of which took much longer than expected to find..

[CODE]
2^353-4203
=
125269909676882800262400105725282077739582106921689791
*
146467647140855997175976549181141923664201888942622379

2^353+20321
=
107212617965684231006696661224016764909923510204087201
*
171136469531909496395965898436670289930931414420683713

2^355-6237
=
201078246063474095502015538594857010445540999246436799
*
364992022501105116452215910637465538969268898994717469

2^355+11609
=
212926542994048279183611705107994489885983607534577991
*
344682042359245646786699688221203535450205665111934047

2^357-84009
=
453147361357734286103874959805167254938456672363539113
*
647841845458687143039115572227866832044273303789018751

2^357+293447
=
470652756196708146570444118328602847134424064755521003
*
623746103643411393320202884671105782953351092003850773
[/CODE]

None of these were in the factordb before at least, so they may be new.

[QUOTE=swishzzz;576780]Test run of Amazon EC2 free tier. A 103 digit snfs job with factmsieve.py takes around 2.5 hours on a single t2 micro Windows instance running at 10% CPU capacity, perhaps this will be faster on a Linux instance with CADO.

[CODE]
2^339 + 15885

Sat Apr 24 15:56:40 2021 p51 factor: 887592350957138861091733941658539740396245192826267
Sat Apr 24 15:56:40 2021 p52 factor: 1261696734859514200896533536322632897894845904544119
[/CODE][/QUOTE]

2^339 ± c completed:

[CODE]
2^339 - 27235 =
967306904908920452789078319450002924493095732788319 *
1157721882688666313356029082874219101278312435085187
[/CODE]

Four more base-2 brilliant numbers:

[CODE]
2^359-123577
=
818923988648227215894707705730371540540812518512510431
*
1433919762596343433061717035212209825301021813200029081

2^359+14621
=
1005099120748900459161798514928920510471822535126047147
*
1168313917648207456964919118126527398761685430631874647

2^361-6273
=
1560537277762292011030721646497096890825992876952316309
*
3009915387784249643267311161037214234010646089476820931

2^361+44571
=
1588267509671791256308972554753220446511580018944216381
*
2957364006343175263301783757664193291901358679995452983

[/CODE]

Proof files are attached.

And another batch finished:

[CODE]
2^363-291
=
4094013899900989030912375965276208433376145195035983021
*
4589222489607338458027850363512336418671632190977908977

2^363+163109
=
3594544799178917497808832006387639836453189974351828487
*
5226904020359514021042583817732061323376054356093003891

2^365-21055
=
6610188871706148247866877699982575091248185129696213497
*
11369321528836272916753163939935476417901514113750418441

2^365+25151
=
6975722917193176731536583299621002374191571619112667517
*
10773559033362830224264470417875672248024627915449550699
[/CODE]

Proof files are attached.

[QUOTE=Branger;591248]Proof files are attached.[/QUOTE]

Well, apparently not. Let's try that again.

Brilliant 201-digit number (10^201-c)
 

"Releasing" 10^201-c.
Tested any 1 <= c <= 40000.

Releasing 10^199+c as well. No p100 * p100 found from 0 < c < 100000.

After a lot of work by Eric Jeancolas, the table of minimal and maximal base-2 brilliant numbers is complete up to exponent 400, as you can see at [url]https://www.alpertron.com.ar/BRILLIANT2.HTM[/url].

Two more for the table:

[CODE]

10^181-28457
=
1976780995904575262824882988600377384132720583677328095507348810273221986844127586224818989
*
5058729328498020382937746413638967841933983271360558098096714142401565169191733122358525587

10^181+38439
=
1054300060000730056488062242818121661270786887706547586912142454641191605667380983978269333
*
9484965788575479583285807708150981397722931500035054082588713947753467817475117863857748683
[/CODE]

Proof files are attached.

I'm still working on 10^221+c, and I'm currently at about c=27000. It is slow going, however, so I will have to see how long my patience lasts.