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2020-10-13, 14:13   #430
Viliam Furik

Jul 2018
Martin, Slovakia

F816 Posts

Quote:
 Originally Posted by retina Okay. Here is a number: 314159265
floor(100000000 * pi)

 2020-10-13, 14:55 #431 LaurV 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
2020-10-15, 00:59   #432
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

32×653 Posts

Quote:
 Originally Posted by Viliam Furik floor(100000000 * pi)
.
Quote:
 Originally Posted by R2357 ... and post a number...

2020-10-15, 07:15   #433
Viliam Furik

Jul 2018
Martin, Slovakia

23×31 Posts

Quote:
 Originally Posted by retina .So what's your new number?
I thought the poster of guessed number is supposed to post a new number. Or is it me who should post number?

2020-10-15, 07:43   #434
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

32×653 Posts

Quote:
 Originally Posted by Viliam Furik I thought the poster of guessed number is supposed to post a new number. Or is it me who should post number?
It's you. Go for it.

 2020-10-15, 08:24 #435 Viliam Furik   Jul 2018 Martin, Slovakia 23·31 Posts Here we go... 3,560,600,696,674
2020-10-15, 16:27   #436
Dr Sardonicus

Feb 2017
Nowhere

3,779 Posts

Quote:
 Originally Posted by R2357 I forgot to post the next number : 30 031
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)

 2020-10-17, 12:12 #437 R2357   "Ruben" Oct 2020 Nederland 2×19 Posts 37*3=111 New number 121
2020-10-17, 13:55   #438
Dr Sardonicus

Feb 2017
Nowhere

3,779 Posts

Quote:
 Originally Posted by R2357 37*3=111 New number 121
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 base-b numbers for any base b > 2.

In decimal, 121 is also 4 less than a cube, 121 + 4 = 53. The only other such number that springs to mind is 4; 4 + 4 = 23. I'll take a guess that 121 is the largest square of an integer with this property.

I renew my offering of 37

2020-10-17, 14:40   #439
Viliam Furik

Jul 2018
Martin, Slovakia

111110002 Posts

Quote:
 Originally Posted by Dr Sardonicus 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 base-b numbers for any base b > 2. In decimal, 121 is also 4 less than a cube, 121 + 4 = 53. The only other such number that springs to mind is 4; 4 + 4 = 23. I'll take a guess that 121 is the largest square of an integer with this property. I renew my offering of 37
Well, it's then either the fact it's the smallest non-supersingular prime, or that it is the mirror of Sheldon prime (73). I guess you meant the former.

 2020-10-17, 17:24 #440 R2357   "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

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