Re: Question on PARI/GP realprecision

[hermann@stamm-wilbrandt.de]

On 2024-03-24 09:53, Karim Belabas wrote:
> If you want to convince yourself that precision is not the culprit,
> compute the sum of the 1/p, instead of 1.0/p. You'll get a *very* large
> rational number, exactly equal to the sum (this is a very wasteful way
> to compute, as the denominator is going to be the product of all primes
> in the list, but it's a doable calculation).
>
> You will then be able to check that this (exactly known) number does 
> not
> belong to your expected interval.
>
> Cheers,
>
>     K.B.
Thanks!

hermann@7950x:~$ gp -q
? #
   timer = 1 (on)
? P=extern("curl -s https://oeis.org/A080076/a080076.json.txt";);
cpu time = 118 ms, real time = 1,417 ms.
? s=0;foreach(P,p,s+=1/p);
cpu time = 18,464 ms, real time = 18,469 ms.
? type(s)
"t_FRAC"
? #digits(numerator(s))
cpu time = 171 ms, real time = 187 ms.
1365297
? #digits(denominator(s))
cpu time = 172 ms, real time = 173 ms.
1365298
? numerator(s)*10^11\denominator(s)
74739239028
?

> Sum_{n>=1} 1/a(n) is in the interval (0.7473924793, 0.7473924795) 
> (Borsos et
> al., 2022). - Amiram Eldar, Jan 29 2022


Regards,

Hermann.