Reverse home primes

themaster · 2008-01-20, 21:29

i really dont know why reverse home primes have never been suggested
there are two ways of doing it that i can think of

reversing the order of the factors:
this would not not work for even numbers but i think there would be a possibility of one iteration being lower than the last which would mean they increase in size a lot slower

it behaves like home primes except that the original composite for each iteration is reversed:
this would be more standard and would work with even numbers

could people post their thought on this and tell which version they prefer or whether we should do both

i have googled "reverse home primes" and it failed to find anything but i am rubbish at selecting keywords so there may already be such a think as reverse home primes

rogue · 2008-01-20, 23:14

How about "neither".

There are enough factoring projects and most have been around for at least 5 years. Personally, I don't think there is anything interesting in the project, although some would argue that most factoring projects are of no interest. Many of the other projects can give users experience with the various factoring algorithms.

BTW, any even number would never have a "reverse home prime", by your definition, because all would end in "2".

tcadigan · 2008-01-20, 23:23

http://www.asahi-net.or.jp/~KC2H-MSM...tha1/index.htm

has a listing of reverse sequences. afaik they're not searched very actively

rogue · 2008-01-21, 00:07

Quote:

Originally Posted by tcadigan

http://www.asahi-net.or.jp/~KC2H-MSM...tha1/index.htm

has a listing of reverse sequences. afaik they're not searched very actively

I don't think that he was referring to the Smarandache search.

tcadigan · 2008-01-21, 01:41

Quote:

Originally Posted by rogue

I don't think that he was referring to the Smarandache search.

ah true....

oh well...better to mention a reverse project that is already defined then start yet ANOTHER search...

roger · 2008-01-21, 03:02

To search for the previous homeprime sequence of a number, you have to parse it. So if you have the number 237, and want to find the previous iteration, it could be one of (2*3*7 = 42) or (2*37 = 74). It cannot be (23*7 = 161) because HomePrimes have to be in ascending order. Otherwise, there would be as many possible next iterations as factors, leading to thousands from a single starting point. Not all (or even most, AFAIK) numbers have more than one possible previous iteration.

You cannot find a previous homeprime iteration for even numbers, because no even number has a previous iteration. (Try finding the previous number for 236

)

You might want to contact Shiva if you're interested. He wrote a quick program to go forwards, as well as search for the previous iterations, which I call ancestors.

Regards,

roger

Phil MjX · 2008-01-21, 20:31

And what about this kind of reverse home primes ?(or haven't I understood the meaning of the first post- ah yes, this was the first possibility).
So, you take the factors from the largest to the smallest (discarding even initial numbers since they'll always be terminating by 2)

Example :

505
101.5

1015
29.7.5

2975
17.7.5.5

etc...

I have written a small gp program a long time ago, as a matter of starting point, and built the complete list up to 1000 in a few cpu hours (up to c60 ?). It should be easy to recompute it.

But I agree that other sequences have a long and interesting history (like the aliquot ones) and I haven't given any cpu time on it since.

A sequence may look as this :

initial number : 505
1 1015
2 2975
3 17755
4 67535
5 1039135
6 3407615
7 6815235
8 138147753
9 4951131713
10 420656910711
11 1696949982633
12 13502035303793
13 89417452343151
14 2184173866935293
15 10583538321924799
16 857926871602101117
17 29521041171916744933
18 634038877932765872977
19 5043783384638611125707
20 247070345532216519297131
21 6875731469757803923895697
22 5905517486204571731097319333
23 20126846259372563172591191111177
24 824860359827212634022499471917119
25 59932749362515763230456219835479109
26 137871148960427447700901794347011671
27 57100729894480499330626801623312389113
28 193987798771599537000937881397368925761
29 441938085026078691207204703167158273133333
30 49917178837038830518331014138227086884379733
31 2291400067682419453718201488033235872916433493
32 10006113832674320758594766323289239619722417229
33 18953510332141525553481008374342905639913910910943
34 103929687369894124130144217491823685879539352066307
35 2640361940402441796507030773529433211299491214991911911
36 141500156963387823067539258554504643505703052731987297333
37 211194264124459437414237699335081557471198586167145219967
38 18367309304819574140233687679124635435338999178949730752033
39 720097897509881856583091892856484335332820988365093332925513
40 20850849559477581108408197504273116080656102935691431493877739
41 1762672725122818293887553459581753494612536609744218414946714917
42 555434289597442305841541956669339403310038575191211238098014639137
43 1915290653784283813246696402308066907965650259280038752062119445329
44 681155670054667252763373316747903013515487484923061709181291113147113
45 579611821441608036363438654961196993106598974409188112238431375979223373
46 222054703906026429166320976121875607558233392354129954915073714109161547777
47 71015887683459966164036200915248295634009438887882414847050729417193050912641
48 149624190629037310529756078246514524049289447172925330221344331718915631559907333
49 319532982552666145520302912912389710545469154001380742673167503543268494059225179313
50 11833439479655944091765320637986910127329967321851419167034535732261372605599473325713
51 30245496777902725274918174894422356200213720753731668606657534890958673963917649761211
52 948635425278304864918033735481730094223398946285678724772877692294723153957348171391723
53 12822943007293978269703390841300681250511443711474027247231729752910588609233874711699310193

Regards.

Philippe.

Phil MjX · 2008-01-21, 20:52

Sorry for the double post :

I have lost rough data, but up to 1000 and almost 70 digits, the remaining "reverse" sequences are (factors from the largest to the smallest) :

starting point, step, composite

209 48 96464039306075871225297292630813197514594470588631068520916401543156157
221 47 11805141358691609289674787018887131523392879983718555192783933137293613
351 43 16141758493799036633337765552219211926947838059358555505815768723118873
505 45 579611821441608036363438654961196993106598974409188112238431375979223373
531 54 10476958472236554174085695162816124340778578978231605152687025363871101
551 43 30285432175153834861052004162627470332567135517003787802641886407148513
559 46 73635827022545513380390651570423794266451230512491027272859971091101943173
585 42 245697610033151679764118755100874649407729620632394283319317201876787147
637 45 2123497257578635107136864678653838501418254770323346982263994160311353733
639 42 53259464628496038177991085391126287752119571476732860749705058316004513
689 37 41542987205715188605918725290182997772575860041385473171138621891576141
695 47 15442911286215714358820897314319037772120547754974481562121195933118173
925 46 12705989670124463997413618564575105302649117298929654210235365921573103
959 45 2123497257578635107136864678653838501418254770323346982263994160311353733

I'll let you reconstruct these sequences and check them for errors as an exercice !

Kind regards and good luck.

Philippe.

Ps : I went a bit farther for the first 4 sequences (as you can see in my first post). Themaster, I'll send you the results if you are interested and you 'd like to go ahead.

themaster · 2008-02-14, 17:34

i have significantly improved the files you gave me and have found all of them up to 200
i am up to:
221 63
351 55
505 69

505 was easy considering its size it now has a c132
i have now run ecm on three of them up to 35 digits

i just reread ur post and realized u had given me to other hard numbers
i will start on them now

sos i forgot to reply thanks for the files

Phil MjX · 2008-02-14, 19:27

Quote:

Originally Posted by themaster

i have significantly improved the files you gave me and have found all of them up to 200
i am up to:
221 63
351 55
505 69

505 was easy considering its size it now has a c132
i have now run ecm on three of them up to 35 digits

i just reread ur post and realized u had given me to other hard numbers
i will start on them now
sos i forgot to reply thanks for the files

Thanks !

I am finishing a gnfs on a c136 aliquot number and, if you are interested, I can offer you some cpu time : I can deal with the c132 with ggnfs if you fail to break it with ecm, or take another sequence up to a larger bound...

Just tell me and, if you want to share, post your progress here.

Regards.

Philippe.

themaster · 2008-02-14, 21:10

i just realized it was a c123 not c132
i have done 35 digit ecm with it
help with the larger composites would be helpful
pm me when u can help

2008-01-20, 21:29	#1
themaster Dec 2007 3³ Posts	Reverse home primes i really dont know why reverse home primes have never been suggested there are two ways of doing it that i can think of reversing the order of the factors: this would not not work for even numbers but i think there would be a possibility of one iteration being lower than the last which would mean they increase in size a lot slower it behaves like home primes except that the original composite for each iteration is reversed: this would be more standard and would work with even numbers could people post their thought on this and tell which version they prefer or whether we should do both i have googled "reverse home primes" and it failed to find anything but i am rubbish at selecting keywords so there may already be such a think as reverse home primes

2008-01-21, 03:02	#6
roger Oct 2006 104₁₆ Posts	To search for the previous homeprime sequence of a number, you have to parse it. So if you have the number 237, and want to find the previous iteration, it could be one of (237 = 42) or (237 = 74). It cannot be (237 = 161) because HomePrimes have to be in ascending order. Otherwise, there would be as many possible next iterations as factors, leading to thousands from a single starting point. Not all (or even most, AFAIK) numbers have more than one possible previous iteration. You cannot find a previous homeprime iteration for even numbers, because no even number has a previous iteration. (Try finding the previous number for 236 ) You might want to contact Shiva if you're interested. He wrote a quick program to go forwards, as well as search for the previous iterations, which I call ancestors. Regards, roger Last fiddled with by roger on 2008-01-21 at 03:03

2008-01-21, 20:31	#7
Phil MjX Sep 2004 5×37 Posts	And what about this kind of reverse home primes ?(or haven't I understood the meaning of the first post- ah yes, this was the first possibility). So, you take the factors from the largest to the smallest (discarding even initial numbers since they'll always be terminating by 2) Example : 505 101.5 1015 29.7.5 2975 17.7.5.5 etc... I have written a small gp program a long time ago, as a matter of starting point, and built the complete list up to 1000 in a few cpu hours (up to c60 ?). It should be easy to recompute it. But I agree that other sequences have a long and interesting history (like the aliquot ones) and I haven't given any cpu time on it since. A sequence may look as this : initial number : 505 1 1015 2 2975 3 17755 4 67535 5 1039135 6 3407615 7 6815235 8 138147753 9 4951131713 10 420656910711 11 1696949982633 12 13502035303793 13 89417452343151 14 2184173866935293 15 10583538321924799 16 857926871602101117 17 29521041171916744933 18 634038877932765872977 19 5043783384638611125707 20 247070345532216519297131 21 6875731469757803923895697 22 5905517486204571731097319333 23 20126846259372563172591191111177 24 824860359827212634022499471917119 25 59932749362515763230456219835479109 26 137871148960427447700901794347011671 27 57100729894480499330626801623312389113 28 193987798771599537000937881397368925761 29 441938085026078691207204703167158273133333 30 49917178837038830518331014138227086884379733 31 2291400067682419453718201488033235872916433493 32 10006113832674320758594766323289239619722417229 33 18953510332141525553481008374342905639913910910943 34 103929687369894124130144217491823685879539352066307 35 2640361940402441796507030773529433211299491214991911911 36 141500156963387823067539258554504643505703052731987297333 37 211194264124459437414237699335081557471198586167145219967 38 18367309304819574140233687679124635435338999178949730752033 39 720097897509881856583091892856484335332820988365093332925513 40 20850849559477581108408197504273116080656102935691431493877739 41 1762672725122818293887553459581753494612536609744218414946714917 42 555434289597442305841541956669339403310038575191211238098014639137 43 1915290653784283813246696402308066907965650259280038752062119445329 44 681155670054667252763373316747903013515487484923061709181291113147113 45 579611821441608036363438654961196993106598974409188112238431375979223373 46 222054703906026429166320976121875607558233392354129954915073714109161547777 47 71015887683459966164036200915248295634009438887882414847050729417193050912641 48 149624190629037310529756078246514524049289447172925330221344331718915631559907333 49 319532982552666145520302912912389710545469154001380742673167503543268494059225179313 50 11833439479655944091765320637986910127329967321851419167034535732261372605599473325713 51 30245496777902725274918174894422356200213720753731668606657534890958673963917649761211 52 948635425278304864918033735481730094223398946285678724772877692294723153957348171391723 53 12822943007293978269703390841300681250511443711474027247231729752910588609233874711699310193 Regards. Philippe. Last fiddled with by Phil MjX on 2008-01-21 at 20:40 Reason: doubts about the first post

2008-01-21, 20:52	#8
Phil MjX Sep 2004 271₈ Posts	Sorry for the double post : I have lost rough data, but up to 1000 and almost 70 digits, the remaining "reverse" sequences are (factors from the largest to the smallest) : starting point, step, composite 209 48 96464039306075871225297292630813197514594470588631068520916401543156157 221 47 11805141358691609289674787018887131523392879983718555192783933137293613 351 43 16141758493799036633337765552219211926947838059358555505815768723118873 505 45 579611821441608036363438654961196993106598974409188112238431375979223373 531 54 10476958472236554174085695162816124340778578978231605152687025363871101 551 43 30285432175153834861052004162627470332567135517003787802641886407148513 559 46 73635827022545513380390651570423794266451230512491027272859971091101943173 585 42 245697610033151679764118755100874649407729620632394283319317201876787147 637 45 2123497257578635107136864678653838501418254770323346982263994160311353733 639 42 53259464628496038177991085391126287752119571476732860749705058316004513 689 37 41542987205715188605918725290182997772575860041385473171138621891576141 695 47 15442911286215714358820897314319037772120547754974481562121195933118173 925 46 12705989670124463997413618564575105302649117298929654210235365921573103 959 45 2123497257578635107136864678653838501418254770323346982263994160311353733 I'll let you reconstruct these sequences and check them for errors as an exercice ! Kind regards and good luck. Philippe. Ps : I went a bit farther for the first 4 sequences (as you can see in my first post). Themaster, I'll send you the results if you are interested and you 'd like to go ahead. Last fiddled with by Phil MjX on 2008-01-21 at 21:15 Reason: PS

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2008-01-20, 23:14	#2
rogue "Mark" Apr 2003 Between here and the 1813₁₆ Posts	How about "neither". There are enough factoring projects and most have been around for at least 5 years. Personally, I don't think there is anything interesting in the project, although some would argue that most factoring projects are of no interest. Many of the other projects can give users experience with the various factoring algorithms. BTW, any even number would never have a "reverse home prime", by your definition, because all would end in "2".

2008-01-20, 23:23	#3
tcadigan Sep 2004 UVic 2×5×7 Posts	http://www.asahi-net.or.jp/~KC2H-MSM...tha1/index.htm has a listing of reverse sequences. afaik they're not searched very actively

2008-02-14, 17:34	#9
themaster Dec 2007 27₁₀ Posts	i have significantly improved the files you gave me and have found all of them up to 200 i am up to: 221 63 351 55 505 69 505 was easy considering its size it now has a c132 i have now run ecm on three of them up to 35 digits i just reread ur post and realized u had given me to other hard numbers i will start on them now sos i forgot to reply thanks for the files

2008-02-14, 21:10	#11
themaster Dec 2007 3³ Posts	i just realized it was a c123 not c132 i have done 35 digit ecm with it help with the larger composites would be helpful pm me when u can help