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Comparative characteristic of various algorithms realized today.
The formula is approximate to the experimental data and computed on a Intel Core2Duo T8300 processor clocked at 2.40 GHz.

Older data computed on Pentium II-400 can be found here.

Legend	Fast algorithm N<95bit	Classical multiplication	Montgomery multiplication	FFT multiplication	Mixed CPU/GPU	GPU implementation

Average value k/sec for 25 < n < 51

n=	24	28	32	36	40	44	48
mmff.exe		1,900,000,000	1,820,000,000	1,600,000,000	1,000,000,000	900,000,000	800,000,000
Fermat.exe	29,750,000	25,000,000	21,600,000	18,700,000	16,750,000	13,500,000	2,700,000
GMP-Fermat	30,000,000	28,000,000	26,000,000	24,000,000	22,500,000	21,000,000	20,000,000
FermFact+PFGW					50,000	50,000	45,000
Ppsieve+PFGW			50,000	60,000	65,000	70,000	65,000

Compare relative speed of different processors with this Excel file.
George Woltman's mmff.exe works for 27<N<174 and k>2²⁴.

Average value k/sec for 50 < n < 1000

n=	54	60	80	100	150	200	300	400	600	800
mmff.exe	750,000,000	650,000,000	350,000,000	300,000,000	130,000,000
Fermat.exe	2,400,000	2,100,000	1,130,000	1,000,000	430,000	300,000	140,000	77,000	31,200	15,700
GMP-Fermat	18,300,000	17,000,000	16,900,000	7,250,000	3,000,000	2,625,000	750,000	450,000	152,000	54,000
FermFact+PFGW	40,000	35,000	30,000	25,000	15,000	14,000	12,000	6,000	2,500	2,000
Ppsieve+PFGW	50,000	45,000	40,000	33,000	22,000	21,000	20,000	15,000	7,500	3,500

Note. For small N, Proth and PFGW are not efficient.
George Woltman's mmff.exe works for 27<N<174 and k>2²⁴.

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	9,000	7,800	1,650	550	150	15	2,3	0.84
GMP-Fermat	31,000	25,000	5,200	1,550	325	43	5	0.84
Proth.exe			555	370	176	51	15	7
FermFact+PFGW	1,300	1,200	600	450	241	89	43	21	5.1	1
Ppsieve+PFGW	1,700	1,600	770	530	255	102	50	25	6	1.2

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

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