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Old 2021-03-29, 14:14   #1
CloudPrime
 
Mar 2021

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Default $100k AWS credits - what are the odds

Hey folks,

So I have $100k in AWS credits that I need to find a good use for. I was tempted to just run folding@home but then I came across the EFF prize for the 100m digit prime and I have to admit it piqued my interest.

Suppose I was to spin up a p4d.24xlarge ec2 instance, I could afford roughly ~3k hours - do you think that would have a decent shot at cracking it - or are there already supercomputers on the job?
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Old 2021-03-29, 14:49   #2
axn
 
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That thing has 8x A100 GPUs and probably 2x 24-core Xeons. Assuming A100 can complete a 100m digit test in 100 hours and 1 socket Xeon can do one in 10 days, you can do about 15 such tests in a week or about 300 in 20 weeks. You will have barely moved the probability needle.
Even if you could somehow reserve one instance for a year, that's still 15*50= 750 tests. Not a realistic way to win EFF prize.

No one is actively pursuing the 100m digit EFF prize - it's a bit of quixotic effort at this point.

Last fiddled with by axn on 2021-03-29 at 14:49
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Old 2021-03-29, 14:52   #3
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However, you are more than welcome to join our pursuit.
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Old 2021-03-29, 15:51   #4
kriesel
 
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Quote:
Originally Posted by CloudPrime View Post
Hey folks,

So I have $100k in AWS credits that I need to find a good use for. I was tempted to just run folding@home but then I came across the EFF prize for the 100m digit prime and I have to admit it piqued my interest.

Suppose I was to spin up a p4d.24xlarge ec2 instance, I could afford roughly ~3k hours - do you think that would have a decent shot at cracking it - or are there already supercomputers on the job?
No. I estimate it falls well short of a "decent shot", if that means more than 1% chance.
Run some rough numbers:
The A100 is rated 746. GHD/d at https://www.mersenne.ca/cudalucas.php
x8 gpus =5968. GHD/d at $32.77/hour https://aws.amazon.com/ec2/instance-types/p4/
It takes ~411. GHD / 103M exponent primality test https://www.mersenne.ca/exponent/103214483
so ~14.52 103M exponents primality tested per day, at $786.48/day cost; $54.16 each exponent. That's far higher per exponent cost than one can achieve owning and running some equipment.
Those that do this sort of thing (GIMPS cloud computing on AWS) would advise to use spot prices instead, which may cost much less.
(Cost is about $1.85 per 103M exponent if you bought a Radeon VII new a couple years ago and live in an area with reasonable utility costs, which soundly beats the spot prices.)
$100k AWS credit would be exhausted at ~1846. primality tests on the service you inquired about, if effort is spent optimally (not leaving a large number of tests partially completed when the credits are exhausted).
Estimated average odds per 100M-332M exponent primality test can be gauged as follows.
Derived from http://hoegge.dk/mersenne/GIMPSstats.html As of 2021-01-27 15:20 UTC
Total number of prime exponents in the interval: 12,125,733
Survived the Mostly Optimal TF & P-1 4,774,303
Mersenne primes expected ~ 3.085 (three)
So estimated probability per TF/P-1 survivor is 0.628ppm. Assume that near 100M those odds are doubled, 1.257ppm. Then the odds of at least one tested exponent of the 1846 being prime assuming close enough to perfect program execution so no errors hide a prime, is ~2319ppm. Finding a prime with that budget and that service is unlikely; ~0.232% chance.
Even if the A100 GHD/d rating is too low by a factor of 2 or 3 the conclusion still holds.
The chance with several already-purchased before the price increases Radeon VIIs and a similar budget at $.12/kw/hr is ~6.8%. Expected return (pretax) is 0.068 * $50k GIMPS prize -$100k cost = $3400-$100k = -$96,600
~0.068 * $3k GIMPS prize -$100k cost = $204-$100k = -$99,796 for 103-332M prime hunting (probability weighted loss). The only known winning economic situation is where someone else is paying the cost, as in Google Colab free. And it doesn't pay much per GIMPS hunter labor hour spent.

We do it for other reasons, not for any reasonable expectation of profit.

Last fiddled with by kriesel on 2021-03-29 at 16:55
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Old 2021-03-29, 15:53   #5
CloudPrime
 
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Quote:
Originally Posted by axn View Post
That thing has 8x A100 GPUs and probably 2x 24-core Xeons. Assuming A100 can complete a 100m digit test in 100 hours and 1 socket Xeon can do one in 10 days, you can do about 15 such tests in a week or about 300 in 20 weeks. You will have barely moved the probability needle.
Even if you could somehow reserve one instance for a year, that's still 15*50= 750 tests. Not a realistic way to win EFF prize.

No one is actively pursuing the 100m digit EFF prize - it's a bit of quixotic effort at this point.
Yikes, that really puts it in perspective. Thanks for crunching the numbers anyway, I really appreciate it!
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Old 2021-03-29, 16:00   #6
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Quote:
Originally Posted by kriesel View Post
No.
Run some rough numbers:
The A100 is rated 746 GHD/d at https://www.mersenne.ca/cudalucas.php
x8=5968 GHD/d at $32.77/hour https://aws.amazon.com/ec2/instance-types/p4/
It takes 411 GHD/exponent https://www.mersenne.ca/exponent/103214483
so ~14.52 103M exponents primality tested per day, at $786.48/day cost; $54.16 each exponent. That's far higher per exponent cost than one can achieve owning and running some equipment.
Those that do this sort of thing would advise to use spot prices instead, which may cost much less.
(Cost is about $1.85 per 103M exponent if you bought a Radeon VII new a couple years ago and live in an area with reasonable utility costs.)
$100k AWS credit would be exhausted at ~1846 primality tests, if effort is spent optimally (not leaving a large number of tests partially completed when the credits are exhausted).
Estimated average odds per 100M-332M exponent primality test can be gauged as follows.
Derived from http://hoegge.dk/mersenne/GIMPSstats.html As of 2021-01-27 15:20 UTC
Total number of prime exponents in the interval: 12,125,733
Survived the Mostly Optimal TF & P-1 4,774,303
Mersenne primes expected ~ 3.085 (three)
So estimated probability per TF/P-1 survivor is 0.628ppm. Assume that near 100M those odds are doubled, 1.257ppm. Then the odds of at least one tested exponent of the 1846 being prime assuming close enough to perfect program execution so no errors hide a prime, is ~2319ppm. Finding a prime with that budget and that service is unlikely; ~0.232% chance.
Even if the A100 GHD/d rating is too low by a factor of 2 or 3 the conclusion still holds.
The chance with several already-purchased before the price increases Radeon VIIs and a similar budget at $.12/kw/hr is ~6.8%. Expected return (pretax) is 0.068 * $50k GIMPS prize -$100k cost = $3400-$100k = -$96,600 (probability weighted loss). The only known winning economic situation is where someone else is paying the cost, as in Google Colab free.
Hm 0.232%.... so you're saying there's a chance? :)

The credits were free through a startup accelerator (AWS Activate perk) but I think I might just have to go with Folding@Home on this one. They're expiring in a couple of months time and we've only used a fraction of the original allocation.

Thanks a million for the breakdown though, really helps me appreciate the monstrous effort involved!

Last fiddled with by CloudPrime on 2021-03-29 at 16:01
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Old 2021-03-29, 16:08   #7
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Quote:
Originally Posted by CloudPrime View Post
Hm 0.232%.... so you're saying there's a chance? :)
Yes. Patrick Laroche found one on his fourth test.
Quote:
Thanks a million for the breakdown though, really helps me appreciate the monstrous effort involved!
You're welcome. We'd be glad to have the help. Can I get that million via Paypal to pay my utility bills and buy more gpus? And air conditioning capacity upgrade, electrical service panel and distribution upgrade.

Last fiddled with by kriesel on 2021-03-29 at 16:11
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Old 2021-03-29, 16:19   #8
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Quote:
Originally Posted by kriesel View Post
Yes. Patrick Laroche found one on his fourth test.You're welcome. We'd be glad to have the help. Can I get that million via Paypal to pay my utility bills and buy more gpus? And air conditioning capacity upgrade, electrical service panel and distribution upgrade.
Haha cheque only I'm afraid, but wait until Friday to cash it if you don't mind!

Part of me is very tempted to take a chance on ~1846 lucky long numbers, but at the same time it seems like an awful waste of electricity. Then again, someone's going to expend it eventually anyway right?
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Old 2021-03-29, 17:04   #9
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Speaking of wastes of electricity, you could burn through $100k of AWS credit by laundering mining it into a smaller pile of cryptocurrency.
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Old 2021-03-29, 17:32   #10
CloudPrime
 
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Quote:
Originally Posted by M344587487 View Post
Speaking of wastes of electricity, you could burn through $100k of AWS credit by laundering mining it into a smaller pile of cryptocurrency.
Against the TOS unfortunately! (AWS Activate specifically, you're free to launder crypto provided you're fronting the cash and not using credits)
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Old 2021-03-29, 17:40   #11
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Use the credits to purchase one of their servers and run it forever.
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