HP49(119)...

[[Leo_01]]

Hello,

Last year, I put 3 pc on this number (hp49.step100) and I ran 2279 curves @ b1=110000000 without succes. (GMP-ECM 5.0.3)
For more detail : http://euclide.euclide.free.fr/hp49/

Cordially
Alex

ps: sorry for my so bad english :-)

[Xyzzy]

Welcome aboard! That is a lot of work!

[[Leo_01]]

Thank you :-)

yes, much of work, without result :-(

Which is the percentage that hp300.step100 breaks up into two prime numbers with one of 55-60 digits? and 60-65 digits?

[sean]

I've done 100 with B1=110e6 and will run more shortly.

[sean]

Alex,

Did you keep your intermediate output from your P-1 effort on HP49.
If you did I could consider pushing the B2 out to 10^15
(or do you not think that is worthwhile?)

Sean.

[akruppa]

Yes, I did. I'm attaching it.

I don't really expect P-1 will find a factor of HP49(100), the time is probably better spent on ECM. Apparantly the prime factors are pretty large, so the better asymptotic complexity of ECM wins by a huge margin.

But if you would like to take a shot at it anyways, be my guest!

Alex

[sean]

For a while now I have been trying the home prime thing in other small
bases. I use the notation HP[b]n to denote the number of steps
to reach the home prime of n in base b. Clearly, HP[b]p=0 for all
bases and primes. But in general, for given n, HP[b]n is different
for different b.

Just like HP49 in the usual decimal base I have found a number of
other recalcitrant cases. The following is a list of first holes.
All are given here in decimal and only the cofactor still to be
factored. If you reserve one I'll send the complete trace for the
case in interest. A few smaller numbers here which people might like
to try with ECM, MPQS, or GNFS.

HP[2]2295 C92 [reserved Irvine]
42593287458358329946084086287073769962120877480092209301263419877966255456101619015115512917

HP[3]64 C137 ecm: [1100@1m][2900@3m][4596@11m]
82655669480551613343580167268477674187351292015117516792944846258008192641612233487099097033209245860710672147412029269159349509639794377

HP[4]66 C114 ecm: [200@250k][2100@1m][2145@3m][1001@11m]
719987348459503015467765102180195287603560808328599685970476462949641504211664952574540740605186353816178317982371

HP[5]21 C125 ecm: [300@250k][1100@1m][2480@3m]
13178488642345386350608829717825621745056764154681613088222022837235795149347293112953213229355932902966772113052923300804587

HP[6]96 C104 ecm: [100@250k][1036@1m]
89766675124873790501352404541149614109540609748271196339218551656401281081928576174053914349607659683071

HP[7]18 C98 ecm: [200@250k][1100@1m][1308@3m]
18544076553116191884123396215530181106075654731696480608775162559674201773848398165459680411817707

HP[8]25 C109 ecm: [100@250k][1100@1m][1229@3m]
5856711191383927187835255094805934789697489673546616834487627675163893104566329958425367249236281881961657743

HP[9]16 C98 ecm: [100@250k][1100@1m]
11458684517279075940009076614278392128600911605811187516921997740429440460654210572105040919082341

HP[10]49 C204 ecm: [9650@43m][2380@110m] P-1:10^11/10^14
346369145517616832561580518436338147877062893457679622195929206654524672587613049343558394373396338194585783775269785675210636696425094776859733305947996048061499249566197147212934512427988113420226762897

[hallstei]

HP[9]16 C98 ecm: [100@250k][1100@1m]
11458684517279075940009076614278392128600911605811187516921997740429440460654210572105040919082341

Using msieve:

Wed May 18 03:57:04 2005 prp40 factor: 1015179412517682216362280776093953604617
Wed May 18 03:57:04 2005 prp59 factor: 11287349187727435902385447478479973049163419264606885870973
Wed May 18 03:57:04 2005 elapsed time 19:15:25

Reserving HP[7]18 C98 :-)

[rogue]

You might also want to consider http://www.angelfire.com/falcon2/hom...oendprime.html, which searches for home primes up to 1000 (base 2).

[hallstei]

Originally Posted by hallstei

HP[9]16 C98 ecm: [100@250k][1100@1m]
11458684517279075940009076614278392128600911605811187516921997740429440460654210572105040919082341

Using msieve:

Wed May 18 03:57:04 2005 prp40 factor: 1015179412517682216362280776093953604617
Wed May 18 03:57:04 2005 prp59 factor: 11287349187727435902385447478479973049163419264606885870973
Wed May 18 03:57:04 2005 elapsed time 19:15:25

Reserving HP[7]18 C98 :-)

Thu May 19 11:42:28 2005 prp42 factor: 371013244266675855845193344908135995895243
Thu May 19 11:42:28 2005 prp56 factor: 49982249527963300183930285965173016012402231268326135649
Thu May 19 11:42:29 2005 elapsed time 26:59:45

[[Leo_01]]

Originally Posted by rogue

You might also want to consider http://www.angelfire.com/falcon2/hom...oendprime.html, which searches for home primes up to 1000 (base 2).

About these numbers, this page is not up to date that should be done in a few days.

hp146 :
500 @ b1=43000000

hp300 :
2440 @ b1 = 3000000
4590 @ b1 = 11000000
2361 @ b1 = 43000000
p+1 : 10^9

All without success :-(
I give up!
If somebody has the desire and the means of continuing...

Alex