By popular demand (almost), here is an overview over where your prime will be listed if it is a factor (a.k.a. divisor) of a Fermat number (F), generalized Fermat number (GF), or extended generalized Fermat number (xGF).

In the following, a question mark (?) denotes any number.

• Your number "is a Factor of F?": Caldwell Fermat, Caldwell general, Keller Fermat
  
• Your number "is a Factor of GF(?,6)": Caldwell GF6, Caldwell general, Keller GF6, Keller general
  
• Your number "is a Factor of GF(?,10)": Caldwell GF10, Caldwell general, Keller GF10, Keller general
  
• Your number "is a Factor of GF(?,12)": Caldwell GF12, Caldwell general, Keller GF12, Keller general
  
• Your number "is a Factor of GF(?,3)": Caldwell GF3, Caldwell general, Keller GF3, Keller general
  
• Your number "is a Factor of GF(?,5)": Caldwell GF5, Caldwell general, Keller GF5, Keller general
  
• Your number "is a Factor of GF(?,7)": Keller GF7, Keller general
  
• Your number "is a Factor of GF(?,11)": Keller GF11, Keller general
  
• Your number "is a Factor of GF(?,8)": Keller general
  
• Your number "is a Factor of xGF(?,?,?)": Keller general
  

One prime can appear many times in Keller's general list (if it divides several of the considered numbers).

To find your row(s) in Keller's long pages, use your web browser to search, in the page, for the exponent n only. For example, if your prime is 31*2^4673544+1, search for 4673544 in the page. If you are the finder (as opposed to the double checker), it should also be possible to search for your surname. Full names are in the bottom of the page.

While Caldwell's pages (the Top Twenties) are generally updated automatically, Keller's pages can take weeks or months before updated.

Additionally, the search here at https://www.primegrid.com/primes/primes.php lets you filter out ((x)G)F divisors as well.

/JeppeSN

Caldwell no longer includes genuine Fermat divisors (first bullet above) in his list "Generalized Fermat Divisors (bases 3,5,6,10,12)" (second link in that bullet). This is more logical. It also corresponds more to what Keller does. /JeppeSN