PARI/GP is based on GMP by default (aarch64/GMP-6.2.1 kernel):Have you compared the speed of pari against gmp/BigNum for factorisation or prime test? I haven't tried gmp with the Pi5 yet, it wasn't very fast on the Pi4, it only uses a single thread.
Code:
? \v GP/PARI CALCULATOR Version 2.15.4 (released) arm64 running linux (aarch64/GMP-6.2.1 kernel) 64-bit version compiled: Dec 9 2023, gcc version 12.2.0 (Debian 12.2.0-14) threading engine: pthread (readline v8.2 enabled, extended help enabled)? https://github.com/Hermann-SW/9383761-d ... -p-1-mod-4
For factoring primes I use multithreaded cado-nfs, that was able to factor RSA-100 on Pi400 in 12.1h first, then overclocked and with a ARM bug I reported fixed, took only 1.8h(!) on Pi400 :
viewtopic.php?p=2124800&hilit=cado+nfs+ ... w#p2124800
Later I did measure factoring times on Pi400 and only 13:30min on overclocked Pi5(!):
Code:
| | Pi400 | Pi5 || RSA | 2.2GHz | 3GHz ||-----+---------+---------+| 100 | 1:49:54 | 0:13:30 || 110 | 4:41:35 | 1:27:27 || 120 | — | 5:05:17 |https://github.com/Hermann-SW/RSA_numbe ... ring-rsa-x
Cool -- how long did the computation take for you on what CPU?I achieved a T5K a couple of weeks ago through SRBase, unfortunately I didn't notice until after the five days registration window so it was then registered as anonymous.
210060*91^331939-1
210060*91^374955-1 was also found by someone else on the same day, I've not seen similar primes occur on the same day before.
Code:
? #digits(210060*91^331939-1)%1 = 650288? http://jpenne.free.fr/
Runs on x86 architecture only because of gwnum lib, which is able to parallelize computation of single multiplication(!) of big numbers.
I learned that I have to force LLR to run on chiplet0 of my 16C/32T 7950X CPU, just did that and proved your number as prime in only 21min ...
Code:
hermann@7950x:~$ taskset -c 0-7,16-23 ./sllr64 -t16 -d -q"210060*91^331939-1"Base factorized as : 7*13Base prime factor(s) taken : 13Resuming N+1 prime test of 210060*91^331939-1 at bit 1005663 [46.55%]Using zero-padded AVX-512 FFT length 288K, Pass1=768, Pass2=384, clm=2, 16 threads, a = 3210060*91^331939-1 may be prime. Starting Lucas sequence... Using zero-padded AVX-512 FFT length 288K, Pass1=768, Pass2=384, clm=2, 16 threads, P = 6210060*91^331939-1 may be prime, trying to compute gcd's U((N+1)/13) is coprime to N!210060*91^331939-1 is prime! (650288 decimal digits, P = 6) Time : 1260.674 sec. hermann@7950x:~$ sCode:
hermann@7950x:~$ ps -o etime= -p 2591 03:20hermann@7950x:~$top - 10:17:39 up 13 min, 2 users, load average: 10.34, 5.59, 2.39Tasks: 464 total, 2 running, 462 sleeping, 0 stopped, 0 zombie%Cpu(s): 0.0 us, 3.7 sy, 25.2 ni, 71.0 id, 0.0 wa, 0.0 hi, 0.0 si, 0.0 stMiB Mem : 31190.9 total, 29557.6 free, 798.1 used, 835.2 buff/cacheMiB Swap: 2048.0 total, 2048.0 free, 0.0 used. 30006.2 avail Mem PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ COMMAND 2591 hermann 39 19 1995820 84544 2816 R 1068 0.3 36:57.92 sllr64 I recently figured out that >950,000 decimal digits are needed to see 16 threads being used:
https://mersenneforum.org/showthread.ph ... post649334
So what do I use PARI/GP for?
Not factoring, and not prime proving.
Although I learned that its precomputed prime tables allow to really fast use of "prime(n)" to compute the n-th prime :
https://pari.math.u-bordeaux.fr/archive ... 00030.html
Code:
pi@raspberrypi5:~ $ freqmin=cur=3000000=maxpi@raspberrypi5:~ $ gp -q -p4M? for(n=1,2^18, prime(n));? ## *** last result: cpu time 1,023 ms, real time 1,028 ms.? prime(2^18)3681131? This small code does compute all xyz coordinates for n=61:
https://github.com/Hermann-SW/GP3D/blob ... gp#L32-L41
Code:
assert(getenv("n")!=0); n=eval(getenv("n")); print("n=",n); assert(n%4!=0&&n%8!=7); Q=qflllgram(get_tqf(n))^-1; M=Q~*Q; S=[x|x<-Vec(qfminim(M,n)[3]),qfeval(M,x)<=n]; jscad.open();https://github.com/Hermann-SW/GP3D/blob ... .gp#L5-L29 )
If I would replace "qfeval(M,x)<=n" by "qfeval(M,x)==n" I would get only those 3-tuples [x,y,z] with x^2+y^2+z^2==n.
I can see those by enabling white sphere surface with radius sqrt(61) for above animation:
- Image may be NSFW.
Clik here to view.
P.S:
One last thing, why did I buy Pi5?
Not because of PARI/GP, hat runs on PiOS as well as faster on x86_64 CPUs.
But wolframscript is free to use on any Raspberry computer, and Pi5 overclocked with 3GHz (I had luck in chip lottery) is 2.8x faster than my Pi400 for long wolframscript computations like:
viewtopic.php?p=2166024#p2166024
Code:
Solve[14*a^2+(130*b+2*c)*a+(302*b^2+101*c^2)==101,{a,b,c},Integers]Statistics: Posted by HermannSW — Tue Feb 06, 2024 9:54 am