Sums of all Squares - Page 2

bsquared · 2010-03-29, 16:46

update...

Code:

found primes in range 30000000000 to 31000000000 in elapsed time = 5.4245
sum of squares complete in elapsed time = 7.1620, sum is 416903941002774697723222981803

found primes in range 31000000000 to 32000000000 in elapsed time = 5.5802
**** 31252968359 is 0 mod 1000000000 ****
sum of squares complete in elapsed time = 7.1759, sum is 457955303775896882861615585442

found primes in range 32000000000 to 33000000000 in elapsed time = 5.5252
sum of squares complete in elapsed time = 7.1461, sum is 501598601070515778427418232428

and another update:

Code:

found primes in range 47000000000 to 48000000000 in elapsed time = 5.5268
sum of squares complete in elapsed time = 7.0336, sum is 1519756369296424391708040649758

found primes in range 48000000000 to 49000000000 in elapsed time = 5.4239
sum of squares complete in elapsed time = 7.0347, sum is 1615357580573805620690452754303

found primes in range 49000000000 to 50000000000 in elapsed time = 5.4835
**** 49460594569 is 0 mod 1410065408 ****
sum of squares complete in elapsed time = 6.8852, sum is 1714863031171407826702942323341

found primes in range 50000000000 to 51000000000 in elapsed time = 5.4299

I'm stupidly using %u to print the modulus, but it is stored internally as a 64 bit integer... so it is only a printing error.

bsquared · 2010-03-29, 22:57

we have this result:

Code:

found primes in range 1915000000000 to 1916000000000 in elapsed time = 5.0965
**** 1915014433303 is 0 mod 1215752192 ****
sum of squares complete in elapsed time = 5.0550, sum is 83903230112675776937166385335972895

So the sum of primes squared up to 1915014433303 is zero mod 100e9. I'm processing about 1 billion numbers per second, so assuming the trend of this sequence holds, to go to the next value at around 20 trillion would take a couple days.

bsquared · 2010-03-30, 02:35

Quote:

Originally Posted by bsquared

...I'm processing about 1 billion numbers per second...

That should have been 1e9 every 10 sec, but the time estimate is still about right. It's probably silly, but a run to 20 trillion is ongoing...

Here was the sum of all prime squares up to 1915014433303:
83775363722237720731978600000000000

I'm keeping a file with the sums every 1e9, in case anyone wants to extend the sequence after I get tired of it or for double checks.

bsquared · 2010-03-30, 12:57

I see that the death knell of this thread has been sounded

Maybe the 12th member of the sequence is still of interest...

$\Sigma_{p = 2}^{4076200167673} p^2 = 786646994677132840800629000000000000$

CRGreathouse · 2010-03-30, 15:07

Quote:

Originally Posted by bsquared

I see that the death knell of this thread has been sounded

Maybe the 12th member of the sequence is still of interest...

$\Sigma_{p = 2}^{4076200167673} p^2 = 786646994677132840800629000000000000$

Are you going to submit this to the OEIS?

bsquared · 2010-03-30, 15:40

I have no problem doing so... but I'm not the "discoverer" of this sequence. I'll defer to you or davar55 if you would rather take the credit.

CRGreathouse · 2010-03-30, 15:44

I PM'd davar55.

bsquared · 2010-03-30, 15:52

Also, this sequence could now be greatly extended.

CRGreathouse · 2010-03-30, 16:12

Quote:

Originally Posted by bsquared

Also, this sequence could now be greatly extended.

Sure. It's quite easy to extend, but tradition limits b-files to 10,000 entries. If you'd like you can extend it to that (or I can), but I wouldn't go beyond. The current b-file has 5000.

As it happens I never computed that sequence for these calculations -- I used pure modular arithmetic. (If I used BCD I could have avoided this while keeping speed high...)

bsquared · 2010-03-30, 17:01

Quote:

Originally Posted by CRGreathouse

Sure. It's quite easy to extend, but tradition limits b-files to 10,000 entries. If you'd like you can extend it to that (or I can), but I wouldn't go beyond. The current b-file has 5000.

I guess I was thinking of a link to tables, or something. But that would require me to generate and host those tables. I'll save that for some day when I'm bored ;)

Quote:

Originally Posted by CRGreathouse

As it happens I never computed that sequence for these calculations -- I used pure modular arithmetic. (If I used BCD I could have avoided this while keeping speed high...)

Yeah, that's definitely faster, but using pure modular arithmetic would require you to start the sum over for each new modulus, right?

CRGreathouse · 2010-03-30, 17:17

Quote:

Originally Posted by bsquared

Yeah, that's definitely faster, but using pure modular arithmetic would require you to start the sum over for each new modulus, right?

Right. You could do two modili at a time without much penalty, though, with appropriate lookup tables and bit operations. Note that you only need to compare (and hence reduce) every 8 primes, each term (other than the first) has index = 5 (mod 8).

2010-03-29, 22:57	#13
bsquared "Ben" Feb 2007 3·1,171 Posts	Right on cue we have this result: Code: found primes in range 1915000000000 to 1916000000000 in elapsed time = 5.0965 ** 1915014433303 is 0 mod 1215752192 ** sum of squares complete in elapsed time = 5.0550, sum is 83903230112675776937166385335972895 So the sum of primes squared up to 1915014433303 is zero mod 100e9. I'm processing about 1 billion numbers per second, so assuming the trend of this sequence holds, to go to the next value at around 20 trillion would take a couple days.

2010-03-30, 15:40	#17
bsquared "Ben" Feb 2007 110110111001₂ Posts	I have no problem doing so... but I'm not the "discoverer" of this sequence. I'll defer to you or davar55 if you would rather take the credit. Last fiddled with by bsquared on 2010-03-30 at 15:40

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2010-03-30, 12:57	#15
bsquared "Ben" Feb 2007 110110111001₂ Posts	I see that the death knell of this thread has been sounded Maybe the 12th member of the sequence is still of interest... $\Sigma_{p = 2}^{4076200167673} p^2 = 786646994677132840800629000000000000$

2010-03-30, 15:44	#18
CRGreathouse Aug 2006 3×1,993 Posts	I PM'd davar55.

2010-03-30, 15:52	#19
bsquared "Ben" Feb 2007 3×1,171 Posts	Also, this sequence could now be greatly extended.