30-120 seconds sounds surprisingly long for ~368 attempts, do you know which part(s) the slowness comes from?

> Miller-Rabin primality test (40 rounds, ~10^-24 false positive rate)

It's way better than that. You are using the simplest upper bound for the false positive rate, which is 1/t^4 where t is the number of rounds. More sophisticated analysis can give better bounds.

See the paper "Average Case Error Estimates for the Strong Probable Prime Test" by Ivan Damgård, Peter Landrock and Carl Pomerance, in Mathematics of Computation Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer (Jul., 1993), pp. 177-194. Here's a PDF: https://math.dartmouth.edu/~carlp/PDF/paper88.pdf

Here are the bounds given there for t rounds testing a candidate of k bits. I'll give them as Mathematica function definitions because I happen to have them in a Mathematica notebook.

1. This one is valid for k >= 2.

  p1[k_, t_] := k^2 4^(2 - Sqrt[k])

Note this one does not depend on t, and for small k does not give a very useful bound. For 160 the bound is 0.00992742. For large k the story is different. Testing an 8192 bit number this gives a bound of 3.45661 x 10^-46. That's good enough for almost all applications so in most cases if you want an 8192 bit prime one round is good enough.

2. This one is for t = 2, k >= 88 or 3 <= t <= k/9, k >= 21.

  p2[k_, t_] := k^(3/2) 2^t t^(-1/2)  4^(2 - Sqrt[t k])

For k = 160 this is valid for 2 <= t <= 17. For t = 17 it gives 4.1 x 10^-23.

3. This one is for t >= k/9, k >= 21.

  p3[k_, t_] := 
 7/20 2^(-5 t) + 1/7 k^(15/4) 2^(-k/2 - 2 t) + 12 k 2^(-k/4 - 3 t)

For k = 160 this is valid for t >= 18. At 18 it gives 9.75 x 10^-26. At 40 it gives 1.80 x 10^-41.

4. This one is for t >= k/4, k >= 21.

  p4[k_, t_] := 1/7 k^(15/4) 2^(-k/2 - 2 t)

For k = 160 this is valid for k >= 40. At 40 it gives the same bound as p3.

So bottom line is that with your current 40 rounds your false positive rate is under 1.80 x 10^-41, considerably better than 10^-24.

If 10^-24 is an acceptable rate for this application, 18 rounds is sufficient giving a rate under 9.7 x 10^-25.

BTW, the larger the k the lower the rate. I've often seen people looking for 1024+ bit primes doing 64 or more rounds. The simplest 1/4^t bound gives 2.9 x 10^-39. OpenSSL for example does 64 for k up to 2048, and 128 for larger k.

For k = 1024 a mere 6 rounds beats that with a bound of 8.8 x 10^-41.

For k = 2048 it only takes 3 rounds to get 4.4 x 10^-41.

For k = 4096 a mere 2 sounds gives 3.8 x 10^-48.

If we had a population of 1 trillion people, each using 1000 things that needed a 4096 bit prime, and that frequently rekeyed so they needed 1000 new primes per second, and every star in the observable universe also had such a civilization consuming 4096 bit primes at that rate, and they were all using 2 rounds of Miller-Rabin, there would be around 24 false positives a year across the whole universe.

If everyone upped it to 3 rounds there would, across the whole universe, be a false positive approximately every 44 billion years.

Sure hope the first line of that bash script isn’t rm -rf $HOME/*

Please don’t ever suggest to anyone ever to curl a script and pipe it to bash. I’m sure this one is fine (I haven’t looked) but it’s a pretty awful idea. Only way to make it worse is to suggest slapping sudo in front.

I think item IDs here are sequential, including comments, so you could have timed the submission to attempt to get one. More likely to get it when the site's quieter.

Pointless yes, but not as aesthetically pleasing at least for me.

This way you can have a choice a ordered primes based on none. Good mood? I’ll go with nonce 773 today.

I made it for you

Hisenprime.

Wolfram alpha thinks it's prime: https://www.wolframalpha.com/input?i=factor+0xcb80ebbd975f00...

Bug, or just a example text bug. Now fixed

I came here to write that :-)

Even with git-prime reducing the address space by a few orders of magnitude, there's still (effectively) zero chance for collision. The difference between 10^-29 and 10^-27 isn't that great in practice.

Just be aware that there are more prime hashes than there are hashes with a specific 2 hex-digit prefix, so even relatively short messages will be much harder to find.

Cute. 8008CAFE

Could you explain what a git trailer is if not appended to the message body? My understanding is that trailers are just key-value pairs in a particular format at the end of the message; there's not an alternative storage mechanism.

Even so, trailers or message body might be moot - rerolling the committed at timestamp should be sufficient!

  Subject ...

  Body body body
  body body ...

  Signed-off-by: ...

It is a trailer; see the source code, line 100:

            message = f"{base_message}\n\ngit-prime Nonce: {attempt}"

I'm not sure whether that's a valid header name, with the space and all, but I remarked on that in another comment already.

It is now a proper git trailer, I think.

No but perhaps you can create at git-coin command?

I added three new options

  --difficulty <leading zeroes>

  --prefix <leading digits>

  --hex-prefix <leading hex digis>

Be warned tho, this makes it excessively hard. It takes a long long time.

We do. Unless I’m mistaken?

I added the trailer syntax, and rewrote git-prime history to ensure all commits are now number theoretic certified.

If you wish to do the same in your own repo I added a script "make-whole.sh" to do this - but I don't recommend it as force pushes and history rewrites could break stuff.

Also added a new tool

  git prime-log

To show which commits are already prime.