
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 512020 digits. This is increasing at roughly 50,000 digits per
year. Click on the trends tab above to view the change over the last few
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 thousands of 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 
425548 
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 
6 
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 
3021 
Consecutive primes in arithmetic progression (4,d=*) 
5 
5 
1209 
Consecutive primes in arithmetic progression (5,d=*) 
5 
5 
1000(*) 
Consecutive primes in arithmetic progression (6,d=*) 
5 
1 
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 
176118 
Divides Fermat 
20 
20 
275977 
Divides GF(*,10) 
20 
20 
340432 
Divides GF(*,12) 
20 
20 
451509 
Divides GF(*,3) 
20 
23 
371306 
Divides GF(*,5) 
20 
20 
404389 
Divides GF(*,6) 
20 
20 
455479 
Divides Phi 
20 
20 
25088 
ECPP 
20 
257 
2051 
Euler Irregular primes 
20 
20 
2188 
Factorial 
20 
20 
7053 
Fibonacci cofactor 
20 
20 
1000(*) 
Fibonacci Number 
20 
13 
5939 
Fibonacci Primitive Part 
20 
20 
1000(*) 
Gaussian Mersenne norm 
20 
16 
396957 
Generalized Cullen 
20 
20 
1884293 
Generalized Fermat 
20 
1684 
16185 
Generalized Lucas Number 
20 
28 
25140 
Generalized Lucas primitive part 
20 
20 
42480 
Generalized Repunit 
20 
20 
1067588 
Generalized Unique 
20 
82 
417693 
Generalized Woodall 
20 
20 
3734 
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 
11631 
Lucas primitive part 
20 
20 
227832 
Mersenne 
20 
20 
7551 
Mersenne cofactor 
20 
20 
466004 
Nearrepdigit 
20 
23 
220285 
Palindrome 
20 
21 
11138 
Partitions 
20 
20 
1750 
Primorial 
20 
20 
3503 
Quadruplet (1) 
5 
5 
3503 
Quadruplet (2) 
5 
5 
3503 
Quadruplet (3) 
5 
5 
3503 
Quadruplet (4) 
5 
5 
1543 
Quintuplet (1) 
5 
5 
1543 
Quintuplet (2) 
5 
5 
1543 
Quintuplet (3) 
5 
5 
1543 
Quintuplet (4) 
5 
5 
1543 
Quintuplet (5) 
5 
5 
1000(*) 
Repunit 
20 
2 
1002 
Septuplet 
5 
5 
1037 
Sextuplet 
5 
5 
43080 
Sophie Germain (2p+1) 
20 
20 
43079 
Sophie Germain (p) 
20 
20 
11050 
Triplet (1) 
5 
5 
11050 
Triplet (2) 
5 
5 
11050 
Triplet (3) 
5 
5 
46873 
Twin (p) 
20 
20 
(**) 
Twin (p+2) 
(**) 
20 
6912 
Unique 
20 
20 
1000(*) 
Wagstaff 
20 
10 
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: 20220516 23:37:15


* old special cases (1), APRCL assisted (1), Cyclotomy Proof (16), Multifactorial (4)
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 (4)
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.