TF Credit oddities

[Christenson]

Hi:

I am running manual tests on a low-end GPU (mfaktc 0.16p1 on Galaxy GEForce210, with CUDA capability 1.2), and one core of a standard AMD 6-core CPU on a completely different machine doing TF work.

Primenet seems to be granting the CPU much more credit for easier work than the GPU, as follows from my Primenet results details report:
CPU Name Exponent Result-Type Received age-days Result GHz-Days
Manual testing 82303141 NF 2011-03-28 13:27 6.6 no factor for M82303141 from 2^68 to 2^69 [mfaktc 0.16p1-Win 71bit_mul24] 0.7264
Eric-AMD-6-core 54008443 NF 2011-03-28 18:53 2.6 no factor from 2^68 to 2^69 1.1069

Why is this?

[ATH]

You are testing factors of the form 2*k*p, so for p=82303141 it is less work to factor to 2^69 than for p=54008443:

82303141: k = 2^69 / 2*82303141 = 3,586,107,426,682
54008443: k = 2^69 / 2*54008443 = 5,464,847,508,738

0.7264 credits * 82303141/54008443 = 1,10696 credits.

[cheesehead]

Originally Posted by Christenson

Primenet seems to be granting the CPU much more credit for easier work than the GPU, as follows from my Primenet results details report:
CPU Name Exponent Result-Type Received age-days Result GHz-Days
Manual testing 82303141 NF 2011-03-28 13:27 6.6 no factor for M82303141 from 2^68 to 2^69 [mfaktc 0.16p1-Win 71bit_mul24] 0.7264
Eric-AMD-6-core 54008443 NF 2011-03-28 18:53 2.6 no factor from 2^68 to 2^69 1.1069

Why is this?

As ATH's example illustrates, for TF (unlike other factoring methods, seemingly, at first glance) the work gets "easier" as exponents go higher.

Between any two given powers-of-2, the number of candidate factors for a higher exponent is less than the number of candidate factors for a lower exponent. Thus, if the power-of-2 limits are held constant, TF has fewer and fewer candidates to test as exponents go higher.

There is an O(log exponent) factor in the time needed for each candidate test as exponents go higher, but it is swamped by the 1/n decrease in number of candidates during that progression.