Subject: Re: [math-fun] Fwd: about bugs in mathematica and pari-gp Date: 2019-05-26 07:21 From: Victor Miller <victorsmiller@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com> I think that macsyma is wrong about 93 * 10^9: time ./primecount -n 93000000000 2560462462787 real 0m0.143s user 0m0.106s sys 0m0.004s time ./primecount 2560462462787 93000000000 real 0m0.106s user 0m0.101s sys 0m0.004s time ./primecount 2560462462786 92999999999 real 0m0.106s user 0m0.101s sys 0m0.004s rwg> ? It agrees with (somewhat cajoled) Mathematica: In[159]:= NextPrime@Prime[9299999999] // tim During evaluation of In[159]:= 0.56919,0 Out[159]= 233746743437 The system you are quoting invites confusion of a function with its inverse. I now recall (in the mid 80s) Macsyma computing prime(10^13). Took most of a weekend. I gave the printout (including a garbage collection message) to a class clown type and he surprised me by taking it to school and getting extra credit. —rwg On Sun, May 26, 2019 at 3:54 AM Bill Gosper <billgosper@gmail.com> wrote:

My old Macsyma gets

(c71) PRIME(8200000000);

(d71) 205021987301

(c72) PRIME(9300000000);

(d72) 233746743437

SPlouffe>Hello,

here is a strange bug,

type Prime[8200000000] or Prime[93000000000] in mathematica and your machine will hang forever....

rwg> No, mine is powered by PG&E.

and by a bizarre coincidence, the same thing happens with pari-gp with the value prime(8200000000), I could not test 93 000 000 000 because it is out of reach for pari-gp (I think).

Does anybody has any idea why the programs are bugging on these particular values ?

rwg>NSA back door.

...

In[156]:= Prime[8200000001] // tim

...

During evaluation of In[156]:= 0.539572 (secs)

...

Out[156]= 205021987381 Macsyma took minutes.

Best regards and have a nice day. Simon Plouffe