20201013, 14:13  #430 
Jul 2018
Martin, Slovakia
F8_{16} Posts 

20201013, 14:55  #431 
Romulan Interpreter
Jun 2011
Thailand
3·13·229 Posts 
neeee... that is just a soup of exponents of mersenne primes...
3^2*5*7*127*(17+89+61*127) Hihihi 
20201015, 00:59  #432 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3^{2}×653 Posts 

20201015, 07:15  #433 
Jul 2018
Martin, Slovakia
2^{3}×31 Posts 

20201015, 07:43  #434 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3^{2}×653 Posts 

20201015, 08:24  #435 
Jul 2018
Martin, Slovakia
2^{3}·31 Posts 
Here we go... 3,560,600,696,674

20201015, 16:27  #436 
Feb 2017
Nowhere
3,779 Posts 
It is the first number of the form p# + 1 which is composite.
2 + 1 = 3, 2*3 + 1 = 7, 2*3*5 + 1 = 31, 2*3*5*7 + 1 = 211, and 2*3*5*7*11 +1 = 2311 are all prime, but 2*3*5*7*11*13 + 1 = 30031 is composite, 59*509 37 (and not that it is the first irregular prime) 
20201017, 12:12  #437 
"Ruben"
Oct 2020
Nederland
2×19 Posts 
37*3=111
New number 121 
20201017, 13:55  #438 
Feb 2017
Nowhere
3,779 Posts 
Nice try. Alas, the stated fact doesn't make 37 "special." Every prime p other than 2 or 5 divides some repunit. "Largest prime factor of smallest composite decimal repdigit" is rather contrived. Even "largest prime factor of decimal repdigit triangular number (666) would be better.
But the special property of 37 I have in mind is that it is the smallest prime having  or not having  a special property of recognized mathematical importance which is possessed by some primes. My apologies for not specifying this originally. And, as I already said, it's not that 37 is the smallest irregular prime. As to 121, it is (b+1)^2 or 11^2 in the usual notation of baseb numbers for any base b > 2. In decimal, 121 is also 4 less than a cube, 121 + 4 = 5^{3}. The only other such number that springs to mind is 4; 4 + 4 = 2^{3}. I'll take a guess that 121 is the largest square of an integer with this property. I renew my offering of 37 
20201017, 14:40  #439  
Jul 2018
Martin, Slovakia
11111000_{2} Posts 
Quote:


20201017, 17:24  #440 
"Ruben"
Oct 2020
Nederland
2·19 Posts 
For 121, the property I had in mind was that it's the smallest composite number that must be counted as a possibility when calculating primes such that p=p"#n+x with x<p",
Note, I wrote the smallest composite, and not the smallest nonprime as 1 isn't composite, it is the only nonzero natural number with this property. I didn't find the property for 37, so I guess I can't suggest a new number 
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