
New record prime (GIMPS): 2^{82,589,933}1 with 24,862,048 digits by P. Laroche, G. Woltman, A. Blosser, et al. (7 Dec 2018). 

If you want to quickly find a large prime of the form k^{.}b^{n}+1 or k^{.}b^{n}1; a large pair of twin primes, Sophie Germain primes, or a Cunningham Chain of length two; a large BiTwin chain; or a large and long Cunningham Chain, then the last thing that you should use is Yves Gallot's Proth.exe! I say the last thing because before that you ought to quickly sieve out any k, n values that are divisible by small primes. If n is fixed then this can be done very efficiently, reducing the overall search time. Another advantage of fixing n is that you can have a good idea of the overall probability of a successful search. This program, NewPGen, performs this type of sieving. NewPGen
should be used to throw out candidate k's until the rate at which
it is removing them exceeds the rate at which Proth.exe can perform a
power test. At that point Proth.exe should be used to complete the search, with UsageTo use NewPGen, simply start it up. You can obtain help from the Help menu item, though it ought to be fairly selfexplanatory. Simple enter the name of the file to generate, the values of the base and n to use, the range of k to use, the type of sieve to perform, and press the Start button. The number of k's that can be sieved is dependent upon available memory. The more k's that you sieve, the greater the overall time saved, as more k's are available to be thrown out. Technical SpecificationsNewPGen can currently sieve for the following types of search:
NewPGen can also be used to generate an output file to use with some Primeform searches. These are basically the same as the above, save that a primorial is used:
1,152,921,504,606,846,976 . The maximum candidate divisor for the other sieves is: 140,737,488,355,327 .
The maximum value of n that can be used in a primorial sieve is: 274,579.
To download, choose one of the following: 
Another prime page by Chris K. Caldwell <caldwell@utm.edu> 