F(33) Fermat 33-th
 

is there any software available (for "normal" human beings) that could verify the 33-th Fermat number for primality at least in principle ?

[QUOTE=enzocreti;516592]is there any software available (for "normal" human beings) that could verify the 33-th Fermat number for primality at least in principle ?[/QUOTE]Yes, in principle, as long as you are prepared to wait for a few millennia for the answer.

Ernst's thread may be of interest: [url]https://mersenneforum.org/showthread.php?t=18748[/url]

[QUOTE=xilman;516594]Yes, in principle, as long as you are prepared to wait for a few millennia for the answer.[/QUOTE]That is hardly a normal person. Or maybe you know something you aren't revealing?

:link to a vid of Queen's "Who wants to live forever?":

Right now I estimate that it's possible to do a 2^33-bit convolution in about 250ms on a high-end computer. So that's 4 iter/sec.

2^33 iterations would be 2^31 seconds or about 63 years.

So not quite a few millennia, but not something we'd want to try now.

[QUOTE=Mysticial;516649]2^33 iterations would be 2^31 seconds or about 63 years.[/QUOTE]
Did you do this conversion in your head? Because I get 68 years (with a calculator, natch).

We know (from the past, when we implemented timers and other things in electronic toys we produce here) that there are about 2^25 seconds in an year. So, without calculator, I would have said in a blink, 64 years (31-25=6, 2^6=64).
But the result is indeed 68 (checked axn with my super-accurate windows 7 calcuator, he is lucky this time, I mean axn, not the calculator, I didn't catch him with the wrong answer, but my time will come... hehe)

[QUOTE=axn;516685]Did you do this conversion in your head? Because I get 68 years (with a calculator, natch).[/QUOTE]


No, but I got lazy and used 8 billion instead of 2^33.

[QUOTE=Mysticial;516710]No, but I got lazy and used 8 billion instead of 2^33.[/QUOTE]

An interesting mnemonic device for me is 1 year =π *10[SUP]7[/SUP] seconds.

Actual number is 3.1577*10[SUP]7[/SUP]

[QUOTE=rudy235;516713]An interesting mnemonic device for me is 1 year =π *10[SUP]7[/SUP] seconds.

Actual number is 3.1577*10[SUP]7[/SUP][/QUOTE]

Actually it is 3.1536*10[SUP]7[/SUP] or 3.16224*10[SUP]7[/SUP] for leap year or 3.15576*10[SUP]7[/SUP] for 4-year average.

[QUOTE=rudy235;516713]An interesting mnemonic device for me is 1 year =π *10[SUP]7[/SUP] seconds.

Actual number is 3.1577*10[SUP]7[/SUP][/QUOTE]

[QUOTE=ATH;516727]Actually it is 3.1536*10[SUP]7[/SUP] or 3.16224*10[SUP]7[/SUP] for leap year or 3.15576*10[SUP]7[/SUP] for 4-year average.[/QUOTE]

1 Year = (365 + 97/400) days
1 day =86,400 seconds


(365+97/400)*86400 =3.1557 * 10[SUP]7[/SUP]

=0.45% over π*10[SUP]7[/SUP]