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Exact difference between PPS, PPSE and MEGA
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BurVolunteer tester
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Joined: 25 Feb 20 Posts: 511 ID: 1241833 Credit: 408,345,480 RAC: 23,751

I'm quite sure this was answered somewhere, but I can't find it.
From the stats page it looks like all PPS and MEGA are searching the same k's and similar max values for n. Is the whole range from 0 < n < 3.xM sieved and then MEGA checks larger n while PPS check smaller ones?
What is the exact range of n and is it completely covered?
PPSE appears to seach larger k exclusively?  

ReggieVolunteer moderator Project administrator Volunteer tester Project scientist Send message
Joined: 10 May 14 Posts: 217 ID: 311759 Credit: 200,665,243 RAC: 50

I'm quite sure this was answered somewhere, but I can't find it.
From the stats page it looks like all PPS and MEGA are searching the same k's and similar max values for n. Is the whole range from 0 < n < 3.xM sieved and then MEGA checks larger n while PPS check smaller ones?
What is the exact range of n and is it completely covered?
PPSE appears to seach larger k exclusively?
PPS is for odd k's in 4<k<1200. PPSE is for odd k's in 1200<k<10000. PPSMEGA started searching with PPS k's but was moved to PPSE k's a little while back. Select k's are also being searched in the PPSDIV subproject right now at higher n values. I'm 99% sure the search started at n=10k, but I don't have a source handy for that.
Sieving is complete for 0<n<6M and undergoing for 6M<n<9M. This is being done through the PPSSieve subproject.
The stats pages aren't ideal for this information since it doesn't show gaps between PPS/PPSE and MEGA.  


Well explained.
I believe in the old days, PPS (i.e. 4 < k < 1200) was searched in chunks in an uneven way such that small k were advanced further than large k. This makes sense in many ways, but is hard to manage. The lowest k values reached megaprime domain in PPS, while the other k were far from reaching megaprimes.
The MEGA project was created starting just over the megaprime level (except k that were past that). And the PPSE was created doing small n in 1200 < k < 10000 instead, is you said. A new philosophy was initiated at PPS to try to have a "straight" leading edge, where all k are at the same n simultaneously.
MEGA was later moved to 1200 < k < 10000 to have many new candidates "just over" 10^999999.
It was realized that the new PPS philosophy was bad for Fermat divisor progress (setting low k on halt for several years), and therefore the DIV project was created to focus on 4 < k < 50 (and initially a couple of other magical k values, but those have been abandoned now). It is often forgotten that for two special k, namely k=9 and k=27, we are only considering odd exponents n in DIV. The even n for k=9 must wait; the even n for k=27 have been singly checked, see next paragraph.
For completeness, the multipliers k = 3, k = 27, and k = 121 have special subprojects, namely 321 (here on BOINC) and 27/121 (PRPNet), and in them, both +1 and 1 forms are searched. In 27/121, the double check is left to DIV (27, odd n, +1 form) and PPS (other +1 forms).
/JeppeSN  


It seems for k > 100, there is still a gap between PPS/PPSE leading edges (which are below the megaprime level) and MEGA. For 10 < k < 100, PPS has "caught up" on MEGA, and the gap has been closed. For 4 < k < 10, classical PPS was already over megaprime level before MEGA was created, and MEGA has never searched them, and never will. /JeppeSN  

BurVolunteer tester
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Joined: 25 Feb 20 Posts: 511 ID: 1241833 Credit: 408,345,480 RAC: 23,751

Thanks!  

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Proth Prime Search :
Exact difference between PPS, PPSE and MEGA 