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-   -   31.4 ... 62.8 ... 100 trillion digits of Pi - GWR (https://www.mersenneforum.org/showthread.php?t=25155)

 ATH 2020-11-20 07:01

[QUOTE=Dr Sardonicus;563805]Hmm, rings a bell.[indent][color=darkred]That girl has problems, bein' heard ain't one of 'em .[/color][/indent]-- Ethel Merman, referring to Janis Joplin[/QUOTE]

He was probably refering to:
[indent][color=darkred]Got 99 problems and a bitch ain't one[/color][/indent]- Ice-T 1993

 mackerel 2020-12-03 15:52

[QUOTE=storm5510;563536]Y-Cruncher seems to prefer vast amounts of swap/storage space on drives over lot of RAM.[/QUOTE]
Only just saw this, forgot this forum was here. Y-cruncher would love as much ram as is needed, but in reality no consumer attainable system can possibly have enough ram for the bigger runs. We're talking well into the TB that not even high end servers can reach. And that's putting aside the cost of that much ram even if you could put it in a single system. So the practicality of it is, you have to use some form of swap as a less insane cost substitute, and that is where the optimisation needs to go.

 Xyzzy 2020-12-03 15:57

To prove that you computed [I]x[/I] digits of pi, couldn't you store only a checksum of all of the digits and keep the last digit "for fun"?

:mike:

 xilman 2020-12-03 16:32

[QUOTE=Xyzzy;565140]To prove that you computed [I]x[/I] digits of pi, couldn't you store only a checksum of all of the digits and keep the last digit "for fun"?

:mike:[/QUOTE]Don't see why not. Computing the last digit is much cheaper than computing them all.

 Xyzzy 2020-12-05 14:28

[QUOTE=xilman;565141]Don't see why not. Computing the last digit is much cheaper than computing them all.[/QUOTE]Would the NT community accept the last digit and a checksum as a record? (Say you ran it twice with a different algorithm each time and both checksums matched.)

:mike:

 Uncwilly 2020-12-05 16:58

The last 10 digits and a 128 bit check-sum would be enough, I would suppose.

 retina 2020-12-05 17:10

Digit extraction algorithms exist. So merely producing a few trailing digits wouldn't be enough to prove you computed all the digits up to that point.

A hash of all digits up to your claimed last digit would be suitable IMO.

 R. Gerbicz 2020-12-05 18:08

[QUOTE=Xyzzy;565355]Would the NT community accept the last digit and a checksum as a record? (Say you ran it twice with a different algorithm each time and both checksums matched.)

:mike:[/QUOTE]

[QUOTE=retina;565379]Digit extraction algorithms exist. So merely producing a few trailing digits wouldn't be enough to prove you computed all the digits up to that point.
[/QUOTE]

There is no BBP type formula for Pi in base ten [though there could be], [url]https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula[/url] .
But even giving only the last few bits would enable to provide a fake proof, just give the exact bits from BBP and give a trash hash value. [notice that even giving say hundred consecutive bits of Pi is "easy"].

Much better: if you're claiming a world record then I would choose 1 million random positions and you should give the bits for each of these positions. The check: select say 20-25 positions and verify the bits with BBP. You have an extremely small probability to fake me. This is assuming that when you need multiple bits of Pi then there is no faster method than to use the BBP formula for each position.

 LaurV 2020-12-07 07:41

Group the bytes by 32 or 64 and compute a SHA256 or SHA512 of it. I don't believe anybody would contest that.

 R. Gerbicz 2020-12-07 14:05

[QUOTE=LaurV;565526]Group the bytes by 32 or 64 and compute a SHA256 or SHA512 of it. I don't believe anybody would contest that.[/QUOTE]

So you would accept any(?) hash value as a proof, say claiming 256T digits of Pi, and giving only sha256 as:
[CODE]
a19a6c3a75783b6b5deee64777873ae207764837e769eedbe9b4c485d94b2986
[/CODE]

 LaurV 2020-12-08 07:01

Yep. After I remake the calculus to see if I get the same value... :razz:
I assume somebody verifies this things, anyhow... Or not?

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