Prime factors of googolplex - 10.

[Arkadiusz]

Current status: 34910 known prime factors.

The following numbers should be added.
1) 12004601725189237
2) 180598008966352693
3) 197459648720034803
4) 1344628210313298373
5) 9425856976319889649
6) 29012014452921284053
7) 59520726126001053271
8) 299566939471790319733
9) 364872254227542882241
10) 24821335229720904734707
11) 33680945809553262133489
12) 80442767581388586501601
13) 1900016393894413508477719
14) 402087904383827727065560627
15) 4531530181816613234555190841
16) 361070657184115294983462212929
17) 759144383635787638836170905729
18) 45316978862713868577793720892923
19) 1612816483312672025726565521114761
20) 3151445759294008336434146467746716852125711
21) 8414640003465161203119978906558054839526493
22) 4790817014835738008638872886922952208975172696533
23) 362853724342990469324766235474268869786311886053883
24) 4624740815741021164555032450406356165555243059597323
25) 104815434978475187938266998366364168321238864689893085842524\
9862927198203812672579936297773867
26) 241265254993818769068186290330219165952420015303371226899082\
2306244494738017616736234979312358033162119575067503362223427
27) 360753792291294051374426809723707883244140602770124331911988\
31287911648192680373281921936535843435181632954359677168188643
28) 157793041231623437279937408119546555586267712054762280488959\
320521697937521092276297325262649574267470228259745983773969\
571127099146658127611270714291518805884658999061123143366757



See:
https://oeis.org/A200861
https://oeis.org/A200879

I suggest that these sequences may be useful.

[science_man_88]

Originally Posted by Arkadiusz

Current status: 34910 known prime factors.

The following numbers should be added.
1) 12004601725189237
2) 180598008966352693
3) 197459648720034803
4) 1344628210313298373
5) 9425856976319889649
6) 29012014452921284053
7) 59520726126001053271
8) 299566939471790319733
9) 364872254227542882241
10) 24821335229720904734707
11) 33680945809553262133489
12) 80442767581388586501601
13) 1900016393894413508477719
14) 402087904383827727065560627
15) 4531530181816613234555190841
16) 361070657184115294983462212929
17) 759144383635787638836170905729
18) 45316978862713868577793720892923
19) 1612816483312672025726565521114761
20) 3151445759294008336434146467746716852125711
21) 8414640003465161203119978906558054839526493
22) 4790817014835738008638872886922952208975172696533
23) 362853724342990469324766235474268869786311886053883
24) 4624740815741021164555032450406356165555243059597323
25) 104815434978475187938266998366364168321238864689893085842524\
9862927198203812672579936297773867
26) 241265254993818769068186290330219165952420015303371226899082\
2306244494738017616736234979312358033162119575067503362223427
27) 360753792291294051374426809723707883244140602770124331911988\
31287911648192680373281921936535843435181632954359677168188643
28) 157793041231623437279937408119546555586267712054762280488959\
320521697937521092276297325262649574267470228259745983773969\
571127099146658127611270714291518805884658999061123143366757



See:
https://oeis.org/A200861
https://oeis.org/A200879

I suggest that these sequences may be useful.

forprime(x=1,500000,if((10^100-1)%x==0,print1(x",")))

looks to generate the first sequence, making it a normal for loop generates the second I believe. I figured a few things out first using other PARI scripts.

[Arkadiusz]

The wanted list:

10,451- (11,41) 88919086325289033199.C381
10,753- (3,251) 4519.52711.299566939471790319733.33680945809553262133489.45316978862713868577793720892923.C417
10,813- (3,271) 97561.943081.2115427.364872254227542882241.C503
10,909- (3,9,101,303) 3637.139987.85556852551.759144383635787638836170905729.1612816483312672025726565521114761.C518

[Stargate38]

Why can't I get http://www.alpertron.com.ar/googolm1.pl (prime factors of googolplex-1) to come up? I keep getting an HTTP 500 Error. What's wrong with it?

[Uncwilly]

Originally Posted by Stargate38

Why can't I get http://www.alpertron.com.ar/googolm1.pl (prime factors of googolplex-1) to come up? I keep getting an HTTP 500 Error. What's wrong with it?

Send user Alpertron a PM.

[alpertron]

The error was a missing #!/usr/local/bin/perl in the first line of the script. There was no problem when using the old Web server which had Windows. The new Web server uses Linux and it appears that the first line is mandatory.

[science_man_88]

Originally Posted by Arkadiusz

https://oeis.org/A200861

a email I sent T.D. Noe a while ago now:

it's easy ( must be if I can do it just ask everyone on mersenneforum.org) to show this is a subsequence of the original definition at very least:

we start by proving a^p-1 | a^(px)-1, done this this we continue by showing that a^b-a =a*( a^(b-1)-1) knowing a = 10 and b=10^100, b-1=10^100-1 =px find prime p dividing 10^100-1 and that's proof that it's at least a subsequence. just thought I'd give you a basic concept of how i'd go about proving it.