I made my own conjecture on base 5 and found much more provable like base2.
For now I am around 773700 digits long candidates and slowly rising to 1M :)
Last prime has 358918 digits, and from that point I have silence in "prime music" :) ( when Prime95 start beeping" and in that way say: prime is found :)
314187728^131072+1 GENERALIZED FERMAT :)
93*10^1029523-1 REPDIGIT PRIME
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie!