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Comparative characteristic of various algorithms realized today in the programs for PII-400
The formula is approximate to the experimental data.

Data has been rescaled to a frequency of 400 MHz. Note though that newer processors have a better instruction and data optimization code.

Legends	Fast algorithm N<95bit	Classical multiplication	FFT multiplication

Average value k/sec for 25 < n < 51

n=	24	28	32	36	40	44	48
Fermat.exe	3 100 000	2 600 000	2 220 000	2 000 000	1 750 000	1 580 000	1 360 000
7•10⁷/n	2 920 000	2 500 000	2 200 000	1 950 000	1 750 000	1 590 000	1 450 000
GMP-Fermat	1 450 000	1 325 000	1 225 000	775 000	725 000	625 000	600 000
Proth.exe	250	250	250	250	240	240	230
FermFact+PFGW	5300	5300	5300	5300	5200	5200	5200

Note. Athlon processors work a little faster than Intel processors. For Fast algorithm approximately 35%.
Only Fermat.exe can perform the work for k < 2^62, other programs only k < 2^31.

Compare relative speed of different processors with this Excel file.

Average value k/sec for 50 < n < 1000

n=	54	60	80	100	150	200	300	400	600	800
Fermat.exe	400 000	250 000	200 000	128 000	68 000	36 000	19 000	10 000	4000	2000
13•10⁸/n²	446 000	360 000	200 000	130 000	57 000	33 000	14 500	8100	3600	2000
GMP-Fermat	575 000	525 000	400 000	325 000	125 000	77 500	24 250	15 000	5 000	2 500
Proth.exe	220	220	210	200	190	190	180	170	160	150
FermFact+PFGW	5200	5000	5000	5000	5000	4000	3300	2860	2000	1550

Note. For small n, use Proth, PFGW and others program is not effective.
The relation of speed at n=36 Fermat/PFGW=580; at n=100, Fermat/PFGW=25; at n=800, Fermat/PFGW=1.3.

Average value k/sec for n > 1000

n=	1000	1060	2000	3000	5000	10 000	20 000	30 000	50 000	100 000
Fermat.exe	1050	300	152	50	15
GMP-Fermat	1250	450	175	68	18
Proth.exe	145	110	105	55	16	6	1	0.3	0.14	0.02
NPGen+PRP+Proth	265	145	125	70	32	10	2	1.1	0.38	0.065
FermFact+PFGW	1100	500	270	150	57	16	3.3	1.4	0.45	0.083
13•10⁸/n²	1300	500	325	144	52	13	3.25	1.44	0.5	0.13

Note. For n > 1000, use of Fermat.exe becomes inefficient.

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