"14071725484041641119...(166100 other digits)...89271538459396766869"

This prime's information:

Description: (from blob table id=249)

By the following definition, while finding p[2,17] with p[1,0]=3, p[2,0]=5, and p[3,0]=7, the second smallest prime was discovered as 20356 * p[3,16] * p[1,16] + 1. This is the number. The proof file (2354792 bytes) can be found at [broken link]. The helper file is the same with the helper file for p[2,17], which contains p[3,16] and p[1,16]. Define:
p[i,j]=ABS[1 + 2 * n[i,j] * p[(i + 1) mod 3,j - 1] * p[(i + 2) mod 3,j - 1]],n is the integer with minimum ABS[n] that makes p[i,j] a prime number.
The primality of p[i,j] can be proven using Brillhart - Lehmer - Selfridge algorithm recursively by using p[(i + 1) mod 3,j - 1] and p[(i + 2) mod 3,j - 1] as helper since n is a small integer, by reducing j to 0.
With this idea, taking
p[1,0]=3, p[2,0]=5, p[3,0]=7 - trival prime numbers.
We got the n[i,j] ( columns : j; rows: i):

j	i=1	i=2	i=3
1	1	- 1	- 1
2	- 1	2	- 1
3	- 8	- 10	7
4	- 14	- 3	- 13
5	- 18	24	46
6	24	39	- 32
7	225	- 48	27
8	120	- 76	30
9	- 132	245	- 676
10	316	- 722	65
11	55	- 1197	- 510
12	- 427	- 1716	- 637
13	4651	- 1158	3420
14	- 16337	17640	- 18426
15	- 8915	- 70649	- 31489
16	- 18844	- 92841	124053
17	- 144011	- 8853	- 14042

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.