20220105, 18:41  #12 
Dec 2008
you know...around...
1344_{8} Posts 

20220109, 13:22  #13 
Romulan Interpreter
"name field"
Jun 2011
Thailand
23351_{8} Posts 
Well, my (joke) answer was more along the lines "100 factorial", but thanks for the cycles anyhow (to you and the others)
Trivia: (hihi) Dr.S sent me by PM, long before you posted, the same century you found. I honestly didn't imagine the answer would be so low (actually, didn't think much about). I replied him the same like here. 
20220109, 14:40  #14  
Dec 2008
you know...around...
2^{2}×5×37 Posts 
Quote:
Actually, if you weren't sure whether 100!+/1 were prime or not, you'd have to go for 199!, or 199# (or larger, of course). 

20220109, 15:49  #15 
Feb 2017
Nowhere
3×17×113 Posts 

20220109, 20:12  #16  
Dec 2008
you know...around...
1344_{8} Posts 
Quote:
Quote:
622803914376064301858782434517 + [0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84] BTW, the first one with 19 primes is <= 110885131130067570042700 + [3, 7, 9, 13, 19, 21, 27, 31, 33, 37, 43, 49, 51, 57, 61, 63, 69, 91, 97], see A186311. 

20220114, 00:11  #17 
May 2018
100000010_{2} Posts 

20220114, 06:22  #18 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011011101001_{2} Posts 
Well, talking about 100 years with no primes (i.e. no round century), I think the first gap >= 100 is at 370262.
(in table at position 17) Quick pari code: Code:
p=2; forprime(q=3,10^8,if(qp>=100,print(p);break);p=q) Last fiddled with by LaurV on 20220114 at 06:26 
20220124, 18:27  #19 
May 2018
100000010_{2} Posts 
If it is not required to be between multiples of 100, then there are some interesting spans of 100 numbers with a lot of primes. For example, there are a whopping 19 primes from 2657 to 2753.

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