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Forum: Puzzles 2011-01-23, 03:58
Replies: 183
Views: 14,885
Posted By davar55
From this thread:

From this thread:
Forum: Puzzles 2011-01-23, 03:52
Replies: 183
Views: 14,885
Posted By davar55
Just checking.

Just checking.
Forum: Puzzles 2011-01-23, 03:44
Replies: 183
Views: 14,885
Posted By davar55
I suppose this might be considered more evidence,...

I suppose this might be considered more evidence, huh?
Forum: Puzzles 2010-12-28, 03:00
Replies: 183
Views: 14,885
Posted By davar55
I'll just say here it's not blind and it's not...

I'll just say here it's not blind and it's not faith.

Forgive me my keys.
Forum: Puzzles 2010-12-28, 02:41
Replies: 183
Views: 14,885
Posted By davar55
While proving a few such important sequences...

While proving a few such important sequences infinite might help us
triangulate on the keys - the k-tuples, and the mersennes.
Forum: Puzzles 2010-12-28, 02:38
Replies: 183
Views: 14,885
Posted By davar55
Well, at some point you might expand on your...

Well, at some point you might expand on your suggested application
of that theorem or theorems to help elucidate this thread's questions.
Forum: Puzzles 2010-12-28, 02:21
Replies: 183
Views: 14,885
Posted By davar55
Thanks. That animated google intro made me...

Thanks. That animated google intro made me chuckle.

Now I have some data on prime constellations, the HL conjecture,
and twin primes. Did Dirichlet anticipate the HL k-tuple conjecture?
Forum: Puzzles 2010-12-28, 01:58
Replies: 183
Views: 14,885
Posted By davar55
Could you put a re-phrasing of the k-tuple...

Could you put a re-phrasing of the k-tuple conjecture here?
Forum: Puzzles 2010-12-28, 01:42
Replies: 183
Views: 14,885
Posted By davar55
This would be a good spot to put in a statement...

This would be a good spot to put in a statement of the k-tuple conjecture.

BTW proving my p^p%10^n sequence infinite might instead be a step
toward proving your k-tuple conjecture.
Forum: Puzzles 2010-12-28, 01:12
Replies: 183
Views: 14,885
Posted By davar55
From above: If we prove that...

From above:





If we prove that enough sequences' infinitude (like this one) depends on that k-tuple conjecture, then proving even one of them infinite would
be evidence that all are -...
Forum: Puzzles 2010-12-17, 19:38
Replies: 183
Views: 14,885
Posted By davar55
So what should we call this particular sequence? ...

So what should we call this particular sequence?
I suspect it will turn up hidden numeric treasures.
Forum: Puzzles 2010-12-15, 21:16
Replies: 183
Views: 14,885
Posted By davar55
If you're computing p^p_sum_mods to 10^12, how...

If you're computing p^p_sum_mods to 10^12, how many digits
will the two highest successful values (new multiples of powers
of ten) have, and will these numbers be equal?
Forum: Puzzles 2010-12-13, 13:50
Replies: 183
Views: 14,885
Posted By davar55
The next step would be to filter out to only...

The next step would be to filter out to only values = 0.

But I think you need a double loop.
Forum: Puzzles 2010-12-13, 03:52
Replies: 183
Views: 14,885
Posted By davar55
While this is current, any other mathematicians...

While this is current, any other mathematicians here want
to comment on whether this sequence is provably infinite?
Perhaps by a density heuristic argument?
Forum: Puzzles 2010-12-13, 03:32
Replies: 183
Views: 14,885
Posted By davar55
Well, so far the sequence of sum(p^p)mod(10^n) ...

Well, so far the sequence of sum(p^p)mod(10^n)
(I think it needs a better name) is:

11
751
1129
361649
361649
12462809
12462809
Forum: Puzzles 2010-12-13, 02:13
Replies: 183
Views: 14,885
Posted By davar55
I suppose my batteries would have been sufficient...

I suppose my batteries would have been sufficient to get
that first term, but for the second I would have needed my
home-built multi-precision (computer-resident) calculator,
written in C but...
Forum: Puzzles 2010-12-12, 21:52
Replies: 183
Views: 14,885
Posted By davar55
So far, this (sum p^p) sequence is: 11 751...

So far, this (sum p^p) sequence is:

11
751
1129
361649

Couldn't have done that without a computer.
Forum: Puzzles 2010-12-12, 21:22
Replies: 183
Views: 14,885
Posted By davar55
Something big? Now wouldn't that be cool to see...

Something big? Now wouldn't that be cool to see ...
Forum: Puzzles 2010-12-12, 20:53
Replies: 183
Views: 14,885
Posted By davar55
Another possibly interesting variation: 2^2...

Another possibly interesting variation:

2^2 + 3^3 + 5^5 + ... + p^p = 10mK

What is the smallest prime p such that
the sum of squares of all primes up to p
is a multiple of 10 (or 100 or 1000...
Forum: Puzzles 2010-04-08, 14:28
Replies: 183
Views: 14,885
Posted By davar55
Another way to extend this problem is to use a...

Another way to extend this problem is to use
a base other than ten. I think binary.

2^2 + 3^2 + 5^2 + ... + p^2 = 2mK

What is the smallest prime p such that
the sum of squares of all primes...
Forum: Puzzles 2010-04-06, 20:28
Replies: 183
Views: 14,885
Posted By davar55
With all the work done on the OP, it shouldn't be...

With all the work done on the OP, it shouldn't be too hard
to generalize the problem a bit.

I think cubes.

2^3 + 3^3 + 5^3 + ... + p^3 = 10mK

What is the smallest prime p such that
the...
Forum: Puzzles 2010-03-30, 20:00
Replies: 183
Views: 14,885
Posted By davar55
This is fine work by all of you. If you wish to...

This is fine work by all of you. If you wish to submit the sequence to
oeis, please go ahead. I couldn't do justice to the calculations, which
I'm really impressed by. Joint discovery...
Forum: Puzzles 2010-03-18, 14:32
Replies: 183
Views: 14,885
Posted By davar55
Nice and simple and quick reply -- thanks. ...

Nice and simple and quick reply -- thanks.

I won't ask about extending the list to 10000, etc. .....
Forum: Puzzles 2010-03-18, 14:00
Replies: 183
Views: 14,885
Posted By davar55
Sums of all Squares

2^2 + 3^2 + 5^2 + ... + p^2 = 10mK

What is the smallest prime p such that
the sum of squares of all primes up to p
is a multiple of 10 (or 100 or 1000).
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