pari operation time - Miller Rabin

Setting 1 in the call to ispseudoprime() in Pari/GP will get you a strong pseudoprime test (Miller-Rabin)

Pseudoprime tests are more practical first attempts when dealing with huge inputs ( In this example the number has 632202 decimal digits )

How long did the operation take? ## shows 13 hours 58 minutes

Link and further reading:

• Miller-Rabin [ wikipedia ] 
• Alternative C implementation of Miller-Rabin by W Izykowski

ABC and ABCDN formats for input to LLR and PFGW - numeric construction

With the creation of organised projects for prime number searching, and the retirement of some of the leading C program creators, the knowledge about ABC and ABCDN format is harder to find.

Here I gather a few links (see references) and show a source code sample that will help point you in the right direction.

LLR is great for standard formats (commonly mined prime areas) and is able to cope with many different formats, however where you differ from some of the more common +1 and -1 forms, the following warning is given in the program readme:

- K*b^n+c numbers with |c| < > 1 or k > b^n can only be PRP tested.

If the number is found PRP, the % of factorization is then shown,
     but note that it is relevant only if c == +1 or -1...

References and links:

• LLR implements "Lucas-Lehmer-Riesel" and Proth algorithms - source
• OpenPFGW - source
• OpenPFGW page about ABC and ABC2 and ABCD - text
• Caldwell pages at University of Tennesse at Martin - program links