Boat Load of 2##### +/- primes
 

I'm finding a bunch of ~12900 digit primes of this form, can this be right?

[url]http://factordb.com/listtype.php?t=4&mindig=12930&perpage=5000&start=0[/url]

1100000000681127037 (6###+30#+11#+7#+31)/1623509753<12925> 12925
1100000000681127048 (6###+30#+23#+19#+17#+13#+11#+7#+31)/6564871<12928> 12928
1100000000680962558 (30068+6###)/15034<12930> 12930
1100000000681127040 (6###+30#+17#+13#+11#+7#+31)/18089<12930> 12930
1100000000681131829 (6###+37#+29#+19#+13#+7#+1)/10211<12930> 12930
1100000000681131480 (6###+29#+19#+13#+7#+1)/2069<12931> 12931
1100000000681193346 (6###+23#+1)/317<12932> 12932
1100000000681127034 (68+6###)/34<12933> 12933
1100000000681127135 (54+6###)/24<12933> 12933
1100000000681127145 (84+6###)/42<12933> 12933
1100000000680962562 (36+6###)/6<12934> 12934
1100000000681126897 6###+5###+30#+7##+1<12934> 12934
1100000000681126898 6###+5###+30##+7##+1<12934> 12934
1100000000681126900 6###+30##+7##+5##+1<12934> 12934
1100000000681126908 6###+30#+5##+7#+1<12934> 12934
1100000000681126911 6###+30#+7#+31<12934> 12934
1100000000681127029 6###+30#+31<12934> 12934
1100000000681127038 6###+30#+13#+11#+7#+31<12934> 12934
1100000000681127049 6###+29#+30#+23#+19#+17#+13#+11#+7#+31<12934> 12934
1100000000681127053 6###+31#+30#+29#+23#+19#+17#+13#+11#+7#+31<12934> 12934
1100000000681127122 31+6###<12934> 12934
1100000000681127128 43+6###<12934> 12934
1100000000681127140 67+6###<12934> 12934
1100000000681127151 (128+6###)/2<12934> 12934
1100000000681127152 151+6###<12934> 12934
1100000000681127174 211+6###<12934> 12934
1100000000681127181 6###+5##+181<12934> 12934
1100000000681129987 6###+13#+7#+1<12934> 12934
1100000000681131055 6###+19#+13#+7#+1<12934> 12934
1100000000681132772 6###+47#+37#+29#+19#+13#+7#+1<12934> 12934
1100000000681190612 6###+13#+31<12934> 12934
1100000000681193349 6###+11#+1<12934> 12934
1100000000681193360 7+6###<12934> 12934
1100000000681193367 (3+6###)/3<12934> 12934
1100000000681206829 6###-61<12934> 12934
1100000000681206835 6###-7#-61<12934> 12934
1100000000681207270 6###-89<12934> 12934
1100000000681207313 6###-127<12934> 12934
1100000000681207318 6###-8191<12934> 12934
1100000000681207333 6###-131071<12934> 12934
1100000000681207348 6###-524287<12934> 12934
1100000000681207497 1+6###-2^61<12934> 12934
1100000000681207530 1+6###-2^89<12934> 12934
1100000000681208089 127+6###<12934> 12934
1100000000681208139 8191+6###<12934> 12934
1100000000681208893 131071+6###<12934> 12934

2^127+6###-1

I tested 10 of them and they were all composite. I'd wager they're all broken. Good catch.

[URL="http://factordb.com/index.php?id=1100000000681208089"]This one[/URL] says it has been proven by N+1, whose factorisation relies on [URL="http://factordb.com/index.php?id=1100000000681127151"]this broken one[/URL]. A bit of a mess.

Heheh, I was afraid of that. I was hoping I'd found a new personal record twin in my search:

2#####+2####+2###+1
2#####+2####+2###-1

These don't make any sense, since 2# = 2, and 2## = 2, and so on, ... 2################################### = 2.

The FactorDB's parser is broken.

Yeah, I think it equates 2## as 6, so 2##### becomes 6###, does appear to be generating real numbers.

It may be embedded primorials that it's flagging as prime. I just rattled off these 8800 digit doozies:

2310##-2310#-31
2310##-2310#-127
2310##-2310#-8191
2310##-2310#-131071
2310##-2310#-524287
2310##-2310#-(2^31-1)
2310##-2310#-(2^61-1)
2310##-2310#-(2^89-1)
2310##-2310#-(2^107-1)
2310##-2310#-(2^127-1)

2310##-2310#-(2^2203-1)....you get the idea

What program where you using to do your runs since it's quite obvious that
2310##-2310#-31 is composite. I suspect that the correct syntax for 2310##-2310#-8191
would be (2310#)#-2310#-8191

Just typing them into factordb which is deeming them to be prime

I know that pfgw (which is one of the testing programs) interprets 6## as 30 and not as 6469693230. It does correctly interpret (6#)# so any entry in the database using concatenated # would have to be removed.