
How big is big enough?

Introduction
The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page. To make the top 5000 today a prime must have 458667 digits. This is increasing at roughly 10,000 digits per year. Click on the trends tab above to view the change over the last five years.
Smaller primes, those not large enough to be in the top 5000, may stay on the list if they are in the first few (either 5 or 20). Below we list how large they must be to make our list. But be careful, this is a moving targetevery month the size of these records increase. So if you want to stay on the list for awhile, do not search for a prime with just a few digits more, aim for a few thousand digits more!
Table of minimal sizes
Smallest prime of special forms on the list
(the smallest that make the list on the merit of the indicated comment alone)
digits required 
archivable form or class 
number archived 
number on list 
(**) 
Arithmetic progression (1,d=*) 
(**) 
10 
(**) 
Arithmetic progression (2,d=*) 
(**) 
11 
388342 
Arithmetic progression (3,d=*) 
5 
10 
25992 
Arithmetic progression (4,d=*) 
5 
10 
10377 
Arithmetic progression (5,d=*) 
5 
10 
3019 
Arithmetic progression (6,d=*) 
5 
5 
2271 
Arithmetic progression (7,d=*) 
5 
5 
1014 
Arithmetic progression (8,d=*) 
5 
5 
1014 
Arithmetic progression (9,d=*) 
5 
5 
(**) 
Consecutive primes in arithmetic progression (1,d=*) 
(**) 
5 
(**) 
Consecutive primes in arithmetic progression (2,d=*) 
(**) 
5 
10546 
Consecutive primes in arithmetic progression (3,d=*) 
5 
5 
3020 
Consecutive primes in arithmetic progression (4,d=*) 
5 
5 
1072 
Consecutive primes in arithmetic progression (5,d=*) 
5 
5 
1000(*) 
Cullen primes 
20 
14 
1070 
Cunningham chain (16p+15) 
5 
5 
(**) 
Cunningham chain (2p+1) 
(**) 
5 
1000(*) 
Cunningham chain (32p+31) 
(**) 
1 
10713 
Cunningham chain (4p+3) 
5 
5 
2972 
Cunningham chain (8p+7) 
5 
5 
(**) 
Cunningham chain (p) 
(**) 
5 
1141 
Cunningham chain 2nd kind (16p15) 
5 
5 
63634 
Cunningham chain 2nd kind (2p1) 
5 
5 
10014 
Cunningham chain 2nd kind (4p3) 
5 
5 
2272 
Cunningham chain 2nd kind (8p7) 
5 
5 
(**) 
Cunningham chain 2nd kind (p) 
(**) 
5 
170758 
Divides Fermat 
20 
20 
206075 
Divides GF(*,10) 
20 
20 
266735 
Divides GF(*,12) 
20 
20 
384169 
Divides GF(*,3) 
20 
21 
364778 
Divides GF(*,5) 
20 
21 
368694 
Divides GF(*,6) 
20 
21 
455479 
Divides Phi 
20 
20 
22084 
ECPP 
20 
255 
1391 
Euler Irregular primes 
20 
20 
1000(*) 
Factorial 
20 
19 
7053 
Fibonacci cofactor 
20 
20 
1000(*) 
Fibonacci Number 
20 
11 
5939 
Fibonacci Primitive Part 
20 
20 
1000(*) 
Gaussian Mersenne norm 
20 
16 
367072 
Generalized Cullen 
20 
20 
1843700 
Generalized Fermat 
20 
1282 
16141 
Generalized Lucas Number 
20 
28 
25140 
Generalized Lucas primitive part 
20 
20 
42480 
Generalized Repunit 
20 
20 
1067588 
Generalized Unique 
20 
84 
417693 
Generalized Woodall 
20 
20 
2272 
Irregular Primes 
20 
20 
16625 
Lehmer number 
20 
20 
13754 
Lehmer primitive part 
20 
20 
7824 
Lucas Aurifeuillian primitive part 
20 
20 
6941 
Lucas cofactor 
20 
20 
1001 
Lucas Number 
20 
20 
11557 
Lucas primitive part 
20 
20 
227832 
Mersenne 
20 
20 
6229 
Mersenne cofactor 
20 
20 
414509 
Nearrepdigit 
20 
23 
206565 
Palindrome 
20 
21 
11138 
Partitions 
20 
20 
1368 
Primorial 
20 
20 
3503 
Quadruplet (1) 
5 
5 
3503 
Quadruplet (2) 
5 
5 
3503 
Quadruplet (3) 
5 
5 
3503 
Quadruplet (4) 
5 
5 
1293 
Quintuplet (1) 
5 
5 
1293 
Quintuplet (2) 
5 
5 
1293 
Quintuplet (3) 
5 
5 
1293 
Quintuplet (4) 
5 
5 
1293 
Quintuplet (5) 
5 
5 
1000(*) 
Repunit 
20 
1 
1037 
Sextuplet 
5 
5 
40093 
Sophie Germain (2p+1) 
20 
20 
40093 
Sophie Germain (p) 
20 
20 
10421 
Triplet (1) 
5 
5 
10421 
Triplet (2) 
5 
5 
10421 
Triplet (3) 
5 
5 
42155 
Twin (p) 
20 
20 
(**) 
Twin (p+2) 
(**) 
20 
4361 
Unique 
20 
20 
1000(*) 
Wagstaff 
20 
9 
1000(*) 
Woodall Primes 
20 
19 
(*) Less than the allowed number are known.
(**) These primes do not make the list on their own merits, but make the list because a companion prime does (e.g., a 'Twin (p+2)' will be on the list if and only if the associate 'Twin (p)' prime is.
 Database last updated: 20201022 13:50:08.


Below are the comments that are currently tolerated in the official comment field, but which appear on the list only if the prime is already on the list for some other reason. Note that provers can add unofficial comments that appear on the individual prime's page, but not in the official comment field.
* old special cases (1), APRCL assisted (1), Cyclotomy Proof (16), Multifactorial (3)
The number in parenthesis is the number currently on the list.
Why are there more than allowed of some forms?
What? Sometimes there are more primes on the list than the number allowed for that form? This happens for the following two reasons.
First, any prime in the top 5000 will automatically be archived, and sometimes there are many of the given form that fit there. When these primes get too small for the top 5000, they will be removed from the list. For example, we may not archive any of a certain form (such as generalized uniques), but there may be some on the list because they fit in the top 5000.
Second, a prime outside of the top 5000 may remain on the list due to another comment. For example, for a long time the only Mills' prime on the list was one of the largest known ECPP primes. It was the latter comment that allowed it to remain on the list.