Special whole numbers...

[10metreh]

Originally Posted by Flatlander

... is the first...

...pair of consecutive even numbers which are both divisible by a cube greater than 1.

[Flatlander]

If you say so.
I had:
"... abundant numbers with the same sum of proper divisors, 120."

[Mini-Geek]

Originally Posted by Flatlander

"... abundant numbers with the same sum of [B]proper divisors[/B], 120."

Actually, the sums of proper divisors of the 54 and 56 are 66 and 64, respectively. The proper divisors of a number excludes the number itself (this is what's used in aliquot sequences). The sum of all divisors of 54 and 56 are indeed both 120.

[Flatlander]

Okay. Stupid book!

[tuckerkao]

Same number is written in 2 different bases, it's a super-double only in 1 of the 2 bases.

[dozenal] 65,Ɛ65,Ɛ00 -> 5 * 7 * Ɛ * 11 * 15 * 17 * 100
[decimal] 232,792.560 -> 5 * 7 * 11 * 13 * 17 * 19 * 144

[mart_r]

A fun thread which deserves reviving, methinks.

Here's a number that I hope will increase during the next few years:

1432

[VBCurtis]

OK, I'll bite: How does a number increase? It's a constant, no?

[masser]

Originally Posted by VBCurtis

OK, I'll bite: How does a number increase? It's a constant, no?

It's sort of like rabbits, but very dependent on the numbers involved. When a 5 meets a 5, that's boring. But when a 3 meets a 7, look out! Slap an x-rating on that one and get the kids out of earshot.

[Dr Sardonicus]

Originally Posted by mart_r

A fun thread which deserves reviving, methinks.

Here's a number that I hope will increase during the next few years:

1432

I'm guessing that 1432 is the number of somethings currently known, "somethings" possibly related to factoring or prime proving, and that the hope is that that number goes up.

I did find a mention that it was the number of known hazardous asteroids some time ago, but I don't think that's it.

I came up with the following number when musing about a recent announcement:

20287

[mart_r]

Originally Posted by VBCurtis

OK, I'll bite: How does a number increase? It's a constant, no?

Well, it's about whole numbers, not constants in particular...

Originally Posted by Dr Sardonicus

I'm guessing that 1432 is the number of somethings currently known, "somethings" possibly related to factoring or prime proving, and that the hope is that that number goes up.

It's not about something currently known, not specifically related to prime proving, but at least in general related to factoring. The hope is that that number goes up, well that's essentially what I wrote about it.
Here's a hint: in what subsection of the forum am I most active?

As for 20287, that's also a tough one. 2292^nd prime number, 2⁶*317-1, B8A7 in base 12, can't see anything related to DJT either...

[Dr Sardonicus]

Originally Posted by mart_r

Well, it's about whole numbers, not constants in particular...



It's not about something currently known, not specifically related to prime proving, but at least in general related to factoring. The hope is that that number goes up, well that's essentially what I wrote about it.
Here's a hint: in what subsection of the forum am I most active?

Based on your generous hint, I did a bit of digging, and found that 1432 is the smallest gap size (difference of consecutive primes) whose first occurrence is not yet definitely known. It has been found that the primes p = 84218359021503505748941 and q = p + 1432 are consecutive, but it is not known whether these are the smallest.

As for 20287, that's also a tough one. 2292^nd prime number, 2⁶*317-1, B8A7 in base 12, can't see anything related to DJT either...

To clarify my hint, the "recent announcement" was not related to any number theory related projects discussed on the Forum. However, the fact that the number 20287 is prime is relevant notwithstanding.