Searches are being conducted for prime numbers of the forms k*b^n-1 and k*b^n+1.

Current efforts:

Riesel prime searches of the form k*2^n-1 are coordinated at and managed by No prime left behind and Riesel prime search.  All k<3400 are being searched and double-checked.

"Conjectures 'R Us" project:  This project was started to coordinate Riesel and Sierpinski conjecture searches for all bases (b) where b<=1024 at Conjectures 'R Us.  The Riesel conjecture states that for all odd k < 509203, there exists at least one prime for each k-value for the expression k*2^n-1.  The Sierpinski conjecture states the same for k < 78557 and the expression k*2^n+1.  The conjectures can be generalized for all bases where a proof is needed for a conjectured lowest k that has already been proven composite for all n.

"No prime left behind" project:  This project was started to coordinate Riesel prime searches of the form k*2^n-1 for k=300 thru 1001 at No prime left behind.  This k-range has been substantially ignored by the prime-searching community and we are playing catch up.  The project has now expanded to include all k=300 thru 3400.

Twin prime searches of the form k*2^n-1 and k*2^n+1.  A twin prime is defined as 2 primes with a difference of 2.

Prime quadruplet searches of the form k*2^n-1, k*2^n+1, k*2^n+5, and k*2^n+7.  A prime quadruplet is defined as 4 primes greater than 3 with a total difference of 8.

Prime searches of the form k*10^n-1.  A prime of this form can sometimes be a "near-repeat-digit" prime, which is defined as a prime with all of its digits the same except for one.


Project links:

"Conjectures 'R Us":  Project forum

"No prime left behind": Project forum

Come join us at either project!  There are many files that are already prepared for prime-searching.


Links to detailed info.:

Riesel primes and ranges

Twin primes k < 100K

Twin primes k < 1M and n > 10K

k*10^n-1 primes

Riesel conjectures

Sierpinski conjectures


Notable discoveries:

Over 250 large primes have been discovered that are currently in the top-5000 all-time largest list of primes shown at

The 9th largest twin prime of all time was discovered on 10/11/2007.  It is 1046619117*2^100000-1 and +1.

The 4th largest prime quadruplet of all time was discovered on 10/25/2007.  It is 2722420456827*2^3800-1, +1, +5, and +7.  It is the #1 largest quad ever to contain a Riesel and Proth prime.

The 5th largest prime quadruplet of all time was discovered on 10/17/2007.  It is 477707955423*2^3802-1, +1, +5, and +7.  It is the #2 largest quad ever to contain a Riesel and Proth prime.