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Old 2008-11-10, 18:57   #485
henryzz
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Quote:
Originally Posted by gd_barnes View Post
I have run a check on all k<2M up to n=5K. Karsten, after removing your k's for primes n>5K, I balance exactly with what you have remaining. I'll post all primes and k's remaining for k<1M on the web pages shortly.

One thing that I'll mention: At any time, you could have removed k's that were divisible by 15 where k / 15 still remained. That would have saved you some testing time.

Henry, you'll need to provide me with a list of primes. Preferred would be all primes for n>500 but if you can at least post primes for n>5K, I can balance what you have remaining. Once you do that, I can update the web pages for k=1M-2M.

I show that there are 28 k's remaining at n=5K for k=1M-2M. This count removes k's divisible by 15 if k / 15 is still remaining.

Edit: I can indeed confirm that there are quite a few less k's remaining at the same testing limit for k=1M-2M vs. k<1M. Very unusual!


Gary
i have two files one for all primes n<1000 sorted by k and one with all the primes n>1000 which is below
if you want me to email you the other file i will do
it is 6.6mb uncompressed
Code:
1072468 1006
1606146 1008
1574578 1016
1436120 1027
1560474 1030
1115812 1032
1720724 1034
1487226 1036
1404010 1043
1053682 1047
1346606 1048
1978384 1051
1077094 1060
1116890 1060
1972326 1065
1612900 1069
1841014 1069
1803906 1072
1815456 1072
1521268 1073
1499650 1074
1712340 1077
1480092 1080
1117682 1089
1347010 1094
1026294 1095
1369448 1095
1766032 1095
1169910 1096
1120634 1100
1663490 1117
1962788 1124
1158502 1125
1416270 1128
1860952 1129
1975986 1131
1867308 1138
1608066 1141
1681612 1143
1322764 1144
1972512 1148
1564044 1155
1093986 1165
1197366 1172
1798426 1177
1812858 1180
1245874 1184
1583694 1184
1160416 1195
1882258 1197
1817282 1199
1438618 1202
1079700 1224
1713112 1226
1302742 1236
1897384 1246
1470584 1257
1075182 1260
1872842 1266
1125422 1274
1798116 1276
1763258 1283
1141028 1294
1858156 1295
1488052 1296
1947040 1301
1199456 1315
1025468 1325
1054948 1335
1812988 1342
1991906 1358
1939480 1361
1924970 1368
1132366 1373
1718832 1382
1434526 1384
1612138 1427
1989740 1441
1743476 1451
1293564 1453
1887070 1470
1855566 1480
1715222 1482
1754804 1492
1336570 1520
1175372 1521
1549344 1539
1813116 1578
1290216 1581
1763412 1581
1099662 1590
1928030 1595
1454214 1603
1930270 1607
1684492 1621
1891178 1635
1983490 1637
1839414 1644
1878400 1649
1778098 1655
1847550 1678
1163050 1679
1837428 1683
1991168 1690
1208134 1703
1904388 1705
1783478 1712
1728576 1725
1355924 1741
1615222 1763
1434478 1836
1902052 1875
1587598 1917
1960126 1930
1411736 1952
1903788 1983
1261892 1997
1965872 2001
1571372 2003
1593850 2082
1303160 2098
1754464 2105
1237252 2124
1665414 2124
1401502 2139
1411056 2159
1617984 2159
1163498 2185
1020308 2193
1095700 2202
1035678 2229
1704660 2244
1009860 2246
1159494 2283
1319712 2304
1389108 2339
1883208 2355
1529734 2386
1603160 2415
1079904 2441
1733744 2448
1125670 2482
1380426 2484
1504306 2487
1812242 2532
1643262 2557
1611864 2602
1759328 2605
1169576 2626
1243344 2650
1893444 2669
1525122 2685
1392152 2708
1931208 2742
1946158 2770
1097834 2799
1101552 2862
1741240 2877
1432568 2892
1364474 2904
1070370 2938
1716420 2995
1954284 3094
1508434 3141
1593210 3208
1605302 3215
1219208 3457
1466048 3628
1993850 3631
1859548 3648
1227664 3679
1245410 3778
1117176 3859
1105592 3893
1046944 3909
1961964 4051
1605386 4069
1639034 4204
1024490 4232
1386014 4404
1919064 4422
1131758 4549
1925294 4887
1135190 4936
1304132 4960
1538474 5050
1937250 5176
1493958 5395
1474060 5725
1974600 6093
1461744 6191
1936564 6242
1222984 6658
1824626 6661
1927162 6765
1982148 6953
1359472 7072
1629142 7198
1692630 7299
1532818 7387
1748198 7992
1844870 11022
1152044 11482
1700990 12354
1878582 12950
1588442 14715
i am thinking of doing some base 3 sieving soon how much faster will it be per 1M ks than base 15 to take them to n=25k
if you find no errors in my base15 files i will use the same scripts
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Old 2008-11-11, 05:33   #486
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Quote:
Originally Posted by henryzz View Post
i have two files one for all primes n<1000 sorted by k and one with all the primes n>1000 which is below
if you want me to email you the other file i will do
it is 6.6mb uncompressed
Code:
1072468 1006
1606146 1008
1574578 1016
1436120 1027
1560474 1030
1115812 1032
1720724 1034
1487226 1036
1404010 1043
1053682 1047
1346606 1048
1978384 1051
1077094 1060
1116890 1060
1972326 1065
1612900 1069
1841014 1069
1803906 1072
1815456 1072
1521268 1073
1499650 1074
1712340 1077
1480092 1080
1117682 1089
1347010 1094
1026294 1095
1369448 1095
1766032 1095
1169910 1096
1120634 1100
1663490 1117
1962788 1124
1158502 1125
1416270 1128
1860952 1129
1975986 1131
1867308 1138
1608066 1141
1681612 1143
1322764 1144
1972512 1148
1564044 1155
1093986 1165
1197366 1172
1798426 1177
1812858 1180
1245874 1184
1583694 1184
1160416 1195
1882258 1197
1817282 1199
1438618 1202
1079700 1224
1713112 1226
1302742 1236
1897384 1246
1470584 1257
1075182 1260
1872842 1266
1125422 1274
1798116 1276
1763258 1283
1141028 1294
1858156 1295
1488052 1296
1947040 1301
1199456 1315
1025468 1325
1054948 1335
1812988 1342
1991906 1358
1939480 1361
1924970 1368
1132366 1373
1718832 1382
1434526 1384
1612138 1427
1989740 1441
1743476 1451
1293564 1453
1887070 1470
1855566 1480
1715222 1482
1754804 1492
1336570 1520
1175372 1521
1549344 1539
1813116 1578
1290216 1581
1763412 1581
1099662 1590
1928030 1595
1454214 1603
1930270 1607
1684492 1621
1891178 1635
1983490 1637
1839414 1644
1878400 1649
1778098 1655
1847550 1678
1163050 1679
1837428 1683
1991168 1690
1208134 1703
1904388 1705
1783478 1712
1728576 1725
1355924 1741
1615222 1763
1434478 1836
1902052 1875
1587598 1917
1960126 1930
1411736 1952
1903788 1983
1261892 1997
1965872 2001
1571372 2003
1593850 2082
1303160 2098
1754464 2105
1237252 2124
1665414 2124
1401502 2139
1411056 2159
1617984 2159
1163498 2185
1020308 2193
1095700 2202
1035678 2229
1704660 2244
1009860 2246
1159494 2283
1319712 2304
1389108 2339
1883208 2355
1529734 2386
1603160 2415
1079904 2441
1733744 2448
1125670 2482
1380426 2484
1504306 2487
1812242 2532
1643262 2557
1611864 2602
1759328 2605
1169576 2626
1243344 2650
1893444 2669
1525122 2685
1392152 2708
1931208 2742
1946158 2770
1097834 2799
1101552 2862
1741240 2877
1432568 2892
1364474 2904
1070370 2938
1716420 2995
1954284 3094
1508434 3141
1593210 3208
1605302 3215
1219208 3457
1466048 3628
1993850 3631
1859548 3648
1227664 3679
1245410 3778
1117176 3859
1105592 3893
1046944 3909
1961964 4051
1605386 4069
1639034 4204
1024490 4232
1386014 4404
1919064 4422
1131758 4549
1925294 4887
1135190 4936
1304132 4960
1538474 5050
1937250 5176
1493958 5395
1474060 5725
1974600 6093
1461744 6191
1936564 6242
1222984 6658
1824626 6661
1927162 6765
1982148 6953
1359472 7072
1629142 7198
1692630 7299
1532818 7387
1748198 7992
1844870 11022
1152044 11482
1700990 12354
1878582 12950
1588442 14715
i am thinking of doing some base 3 sieving soon how much faster will it be per 1M ks than base 15 to take them to n=25k
if you find no errors in my base15 files i will use the same scripts


This is a sufficient list of primes for my use. Everything looks great! There are officially 9 k's remaining for k=1M-2M. Can you provide me with an updated test limit? The last that you stated was n=14.4K. Since you have a prime for n=14715, I'll show n=14.7K. I'll update the web pages shortly.

BTW, you need to use a little punctuation. lol I can't tell if your 1st line is making a statement followed by asking a question or if it's just one big run-on sentence that is making a statement with a couple of words left out. If it's a question, can you ask it again?


Gary
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Old 2008-11-11, 06:23   #487
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Quote:
Originally Posted by Flatlander View Post
Well, looking at the top ten primes, I've dusted off my slide rule and calculated that the probability of me finding a prime within weeks/months is exactly:
"Maybe."
But the probability of someone else finding a prime from this file after me is exactly:
"Probably."
That's why I'm sieving even though I'm unlikely to benefit much/at all.
Also, I can't put more than one core on testing because we are looking for the lowest prime.

(Talking of slide rules, I was given one of them to use for my first year at secondary school, then they took them away the next year and told us to buy calculators! Also, at my first school we were taught in imperial units but when I went to secondary school we switched to metric. So I say things like "5 feet and 3 cm".)

btw Searching to n=200k would be 1/9th of the file.

lol, you're right. It is 1/9th of the file! my bad

Why can't you put more than one core on it and still find the lowest prime? Do what I do when I want to test a range and have no gaps while testing: Sort the file into multiple files using a 1, 2, 3, 4, 1, 2, 3, 4, etc. sequence. Here's what I mean:

File one:
k/n pair 1
k/n pair 5
k/n pair 9
etc.

File 2:
k/n pair 2
k/n pair 6
k/n pair 10
etc.

File 3:
k/n pair 3
k/n pair 7
k/n pair 11
etc.

File 4:
k/n pair 4
k/n pair 8
k/n pair 12
etc.

This can be done by a cut-and-paste into Excel column A, then add a column B with 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, etc. in it, and then sort on column B. You don't need a secondary sort because even though all the 1's are the same, Excel doesn't change the position of rows unless the sorting requires it to. So it will keep the file in its original sequence within each occurrence of '1'. The same for each occurrence of '2', '3', and '4'. That way each of the 4 files is still in proper n-value sequence.

That way, you never have gaps in your testing unless one of the testing cores is significantly faster than another. In effect, it somewhat replicates what an LLRnet server does if you had 4 cores on one.

For base 27, you could test n=100K-200K that way. It'd be a lot of work for 1 core but on 4 cores running concurrently at the same n-range such as this, it wouldn't be too bad.

On a related note: I'm kind of tired of my Sierp base 12 effort crawling along on 1 core at n=196K (going to n=250K). At its current rate, it will take ~50-55 CPU days to get it up to 250K. In the next day or 2, I'm thinking of dividing it up on 3 quads with the files split up just like I am showing above. I'll just split it into 12 files using a 1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,etc. sequence. That will knock it out in ~4-5 days if it doesn't find a prime but if it finds one, it will be the smallest. Then I can get back to other stuff and not have it tieing up a core.

I run many of my multi-core conjecture efforts this way. I'm currently running Riesel base 256 on 4 cores this way. It's currently at n=65K with no gaps below or above. If a prime is found, I stop all 4 cores and remove the k from each one of them, which are at the same n-range. The problem with dividing it up by n-range is that in the long run, it takes more CPU time because frequently you will have tested ranges much higher than the prime you find and those tests will have taken much longer. The point being: Those cores on higher ranges could have been used to find the smaller prime much more quickly by using the above tact.


Gary


P.S. BTW, I've actually done this on situations where one machine is significantly faster than another yet managed to keep them testing at the same n-range. The math gets a little tricky when deciding what numbers to put in column B but it can be done. If that is your situation and you want to do this, I could PM you with my method of doing it if you wanted. One thing that is a requirement: After you're done, it's important to merge and resort all of the results files by n-value/k-value to make sure you missed no tests. It's easy to miss or duplicate a result when messing around with resorting files like this.

Last fiddled with by gd_barnes on 2008-11-11 at 06:40
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Old 2008-11-11, 07:26   #488
henryzz
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my current test limit is n=21.5k

i presume it is the text after the primes that is the problem so i will restate that:
I am thinking of doing some base 3 sieving soon. How much faster will it be per 1M ks than base 15 to take them to n=25k?
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Old 2008-11-11, 09:35   #489
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Quote:
Originally Posted by henryzz View Post
my current test limit is n=21.5k

i presume it is the text after the primes that is the problem so i will restate that:
I am thinking of doing some base 3 sieving soon. How much faster will it be per 1M ks than base 15 to take them to n=25k?

I assume no primes since n=14.7K.

Ah, OK. Makes sense now...lol...I can't quite answer your question fully because its dependent on a # of factors such as k-range chosen, how you choose to test it, etc. I will say this:

I think I remember that it generally took me around 1 CPU day to test every 1M k-range of base 3 to n=25K. That would be only 500,000 k's. So it'd be 2 CPU days or so to do 1M k's. Based on my testing of k=2-2M on base 15 to n=5K, I think that took just a little over 1 CPU day. I'd guess another 2-3 CPU days to get it up to n=25K.

Based on that I would estimate that it would take you about 4 times as long to test base 15 as it does to test base 3, both because base 3 is more prime and because its a lower base giving it even more opportunities for small primes. Less k's remaining, less testing time for those k's remaining at the same n-range means a big difference in total testing time. Trying doing a k=1M range like you did for base 15 and see if that's close.

Base 3 has its pros and cons:

Pro: A lot of primes so few k's remaining.

Con: A lot of k's that are powers of 3 times k's that are already remaining. It can be very tricky to weed out the correct k's and remove them. Base 15 is easier in that regard because there are less powers of 15 vs. powers of 3 in any given k-range, i.e. 15, 225, 3375, 50625, etc. vs. 3, 9, 27, 81, 243, 729, 2187, 6561, 19384, 59049, etc. I noticed that both you and Karsten had some k's remaining for a while in your base 15 testing that you didn't need to have but a prime was eventually found for all of them and so you ended up matching what I had remaining. It's not a big deal to be effectively double-testing k's below n=25K. Above that and it's wasting a lot of CPU resources.

Edit: I just now noticed this...Were you referring to sieving or primality testing on base 3 vs. base 15? Sieving would be only a little longer for base 15. Because base 15 is a higher base, you'll need to sieve it a little deeper to get to the optimal depth. Also, there will be more k's remaining within the same k-range. I'd say base 15 would take, perhaps, 30-35% longer than base 3 to sieve the same k-range.


Gary

Last fiddled with by gd_barnes on 2008-11-11 at 09:42
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Old 2008-11-11, 13:46   #490
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Ok. I'll look into doing that on OpenOffice Calc.
(Or Office on the Kids' PC.)
At the moment I'm just sieving because I've already tested 4 unnecessary candidates.
Tested to >111k, sieving at >9T, >300 factors found.

It's difficult to know what is the best strategy with sieving/testing because we are just looking for the first prime. Hence, the uneasy feeling in my stomach that I've just stopped testing right before 'the' prime. lol
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Old 2008-11-11, 17:15   #491
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i dont know why i said sieving i meant primality proving
once my base 15 effort is finished to n=25k i will do 500000 ks from base 3 to n=25k
i have had a rather large gap between primes almost 1/3 of the range tested
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Old 2008-11-11, 18:02   #492
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Quote:
Originally Posted by grobie View Post
I am going to reserve Riesel Base 45 k=24 to n=50k, if I am happy with this computer I might add more k's later.
Range is complete to n=50k, No Primes, let me know if you need the results file.
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Old 2008-11-11, 20:57   #493
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Quote:
Originally Posted by KEP View Post
Well then I think I've an answer to your previously question. Running 1M range (500,000 k's) to n<=25K, will take about 12 hours, if you only use OpenPFGW and starts out by doing some PRP testing at first, and eventually verifies the PRPs. So for administrative purpose i would suggest that you at least reserves 10M ranges or maybe 100M (dependent on the amount of cores you tent to put on this effort). I'm considering to launch an attack on a 1G range as soon as my Quad is done with the few important reservations she is working on This should take about 150 days from start to finish on the Quad (Q6600).

Also I may add, sieving is far more efficient from n>1000 (maybe n>2500) since trial division and factoring then starts to be to time demanding. But for the easyness of creating the proof later on, I'm considering to do it this way:

1. PRP test all k's reserved to n<1000
2. Sieve the k's remaining for n>1000 to n<=25000
3. PRP test all k's remaining in sieve file (for at most 1 prime per k)
4. Proof the PRP with n>1000
5. Proof the PRP with n<=1000
6. Release remaining k's to the public for further testing

This was my humble suggestions, but this seems to be the most efficient, however testing large ranges is with current technology bad, when talking about catching the PRP primes turning out to be actually composites. But the listed way, is the most effecient way and less risky of suffering various delaying setbacks. I've suffered many in my first 500M range, but a lot of new scripts has been developed and this really helps making it easier to go with large ranges.

Also a final notice, I've updated my Rb3a website, and Gary it appears that you've either one of your sites (the one with remaining k's) not updated or you have to many primes on your primelist. To crosscheck, I can mention that I've currently 215 primes listed and 973 k's remaining.

Regards

KEP
thanks i think i will reserve a 10M range when i have a core free then
i only have four cores so i tend to not use more than one occasionally two cores per type of work

i have just found another prime
1570340 21918
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Old 2008-11-14, 04:53   #494
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Quote:
Originally Posted by grobie View Post
Range is complete to n=50k, No Primes, let me know if you need the results file.
Yes, if you could post the results file or Email it to be at: gbarnes017 at gmail dot com ; that would be great.



Gary
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Old 2008-11-14, 04:55   #495
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Sierp base 12 is finally at n=200K...nothing to report; continuing on to n=250K.

Thanks to Max for speedy Phrot! My tests are ~40% faster: 3480 vs. 2090 secs. per test at n=195K!!


Gary

Last fiddled with by gd_barnes on 2008-11-14 at 04:57
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