Special whole numbers...

[Viliam Furik]

Originally Posted by retina

Okay. Here is a number: 314159265

floor(100000000 * pi)

[LaurV]

neeee... that is just a soup of exponents of mersenne primes...

3^2*5*7*127*(17+89+61*127)
Hihihi

[retina]

Originally Posted by Viliam Furik

floor(100000000 * pi)

.

Originally Posted by R2357

... and post a number...

So what's your new number?

[Viliam Furik]

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?

[retina]

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.

[Viliam Furik]

Here we go... 3,560,600,696,674

[Dr Sardonicus]

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)

[R2357]

37*3=111


New number 121

[Dr Sardonicus]

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

[Viliam Furik]

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.

[R2357]

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 non-prime 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