[URL="http://factordb.com/index.php?id=1100000000127077466"](2142175951^19-1)/2142175950[/URL] factors as:
[code]PRP83 = 19113609633955111903782177375948091679207089078350730364061491806823609294931874901
PRP59 = 80474075472503825455998354377166425823095553698559798887137[/code]

I'd like to reserve 76372709981818363434801791580961^7-1 (C140/S192), 53929223^23-1 (C141/S194), 16763^37-1 (C153/S157), and 2273^59-1 (C153/S202), in no particular order.

[QUOTE=Dubslow;314294]
I'd like to reserve 76372709981818363434801791580961^7-1 (C140/S192), 53929223^23-1 (C141/S194), 16763^37-1 (C153/S157), and 2273^59-1 (C153/S202), in no particular order.[/QUOTE]

[URL="http://factordb.com/index.php?query=76372709981818363434801791580961%5E7-1"]Done[/URL], [URL="http://factordb.com/index.php?query=53929223%5E23-1"]done[/URL], [URL="http://factordb.com/index.php?query=http://factordb.com/index.php?query=16763%5E37-1"]done[/URL] and [URL="http://factordb.com/index.php?query=2273%5E59-1"]done[/URL]. Nothing particularly interesting about the factors.

Pascal has asked for assistance clearing Level 5 Roadblocks. Some of these are in the SNFS 200 to 250 digit range and have been added to the RSALS work stream. Three of these are smaller than the RSALS minimum and may be of interest to individuals here. These have had ECM to 2/9 of the SNFS difficulty, the level usually deemed appropriate before SNFS. Post if interested – I will track reservations and progress in this message.
[code]487^73-1 C194 Factored by Mathew
158071^37-1 C188 Factored by Dubslow
200029^37-1 C191 Factored by Dubslow[/code]
Last September we cleared all the [URL="http://www.mersenneforum.org/showthread.php?p=311744#post311744"]“Level 6 Roadblocks”[/URL] in Pascal’s proof that there are no Odd Perfect Numbers less than 10^1600. A Roadblock happens when a factor chain cannot be extended because there are no more known factors. One of the mathematical contributions of Pascal and Michael’s [URL="http://www2.lirmm.fr/~ochem/opn/opn.pdf"]paper[/URL] is a method to continue by considering a set of possible continuations. When one of those possible continuations hits a roadblock, it’s called a Level 2 Roadblock, and can be recursively handled by considering yet another set of possible continuations. This cascade of possible continuations makes the proof tree unwieldy.

I would like to reserve at least the smallest. Depending on the other project I have running at the moment, and how long you're willing to wait, I'd like to do all three of them. But, for now, I'll leave the other two available.

I would like to reserve 487[SUP]73[/SUP]-1

If no one else wants 200029^37-1 I'll do it. It'll be the middle of next week before I get started on it though.

Chris

I should be able to start it by Sunday, whenever the first one finishes.

OK, you can have it.

Chris

[QUOTE=Mathew;323965]I would like to reserve 487[SUP]73[/SUP]-1[/QUOTE]

Complete

[CODE]prp89 factor: 17964306826148107851772118436931721533697423044073497154332006228156760694228028533136357
prp106 factor: 1772423237719597181478072826454099671363987810953239647940491272834023191400051558124317332625061357965773[/CODE]

158071^37-1 factors as:
[code]prp63 factor: 188016886585675974023185085697878053899487272529211250099690199
prp125 factor: 76645227601832863253981911467158876241325886725704878174538411800801086918064627243276801617029101919191556272638581616905943[/code]

I've just started 200029^37-1 -- and if I may make a plug, B[sup]2[/sup]'s new SNFS code is awesometastic :grin: (no thinking required!)

[code]./yafu "snfs(200029^37-1, (200029^37-1)/(2^2*3*79*211))" -threads 8


01/14/13 00:45:31 v1.33 @ Gravemind, System/Build Info:
Using GMP-ECM 6.4.3, Powered by GMP 5.0.4
detected Intel(R) Core(TM) i7-2600K CPU @ 3.40GHz
detected L1 = 32768 bytes, L2 = 8388608 bytes, CL = 64 bytes
measured cpu frequency ~= 3392.306290
using 20 random witnesses for Rabin-Miller PRP checks

===============================================================
======= Welcome to YAFU (Yet Another Factoring Utility) =======
======= bbuhrow@gmail.com =======
======= Type help at any time, or quit to quit =======
===============================================================
cached 78498 primes. pmax = 999983


>> nfs: checking for job file - job file found, testing for matching input
nfs: number in job file does not match input
nfs: checking for poly file - no poly file found
nfs: commencing nfs on c197: 13817824122658419547399851017557180330278983713767365721715619950128113918378644044199224283682279984169863968440019858817534432706309179958135262942735575203332682472043807416507625261347929241708
nfs: searching for brent special forms...
nfs: input divides 200029^37 - 1
gen: ========================================================
gen: considering the following polynomials:
gen: ========================================================

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 212.04, anorm: -1.76e+41, rnorm: 3.00e+47
type: snfs
size: 212
skew: 72.9989
c5: 1
c0: -8003480504624389
Y1: -1
Y0: 2562971107509130104661660981719822340812961
m: 2562971107509130104661660981719822340812961

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 206.74, anorm: -6.05e+30, rnorm: 1.47e+44
type: snfs
size: 206
skew: 0.0076
c5: 40011600841
c0: -1
Y1: -1
Y0: 12812997652885982055910197929899276309
m: 12812997652885982055910197929899276309

Error: M=12812997652885982055910197929899276309 is not a root of f(x) % N
n = 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
f(x) = + 1*x^6 + 0*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 - -9223372036854775808*x^0
Remainder is 320232058066384270446735341

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 201.44, anorm: -3.20e+33, rnorm: 1.77e+38
type: snfs
size: 201
skew: 0.1308
c6: 200029
c0: -1
Y1: -1
Y0: 64055700187902664393213973623321
m: 64055700187902664393213973623321


gen: ========================================================
gen: best 3 polynomials:
gen: ========================================================

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 201.44, anorm: -3.20e+33, rnorm: 1.77e+38
# scaled difficulty: 207.53, suggest sieving rational side
type: snfs
size: 201
skew: 0.1308
c6: 200029
c0: -1
Y1: -1
Y0: 64055700187902664393213973623321
m: 64055700187902664393213973623321

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 206.74, anorm: -6.05e+30, rnorm: 1.47e+44
# scaled difficulty: 219.58, suggest sieving rational side
type: snfs
size: 206
skew: 0.0076
c5: 40011600841
c0: -1
Y1: -1
Y0: 12812997652885982055910197929899276309
m: 12812997652885982055910197929899276309

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 212.04, anorm: -1.76e+41, rnorm: 3.00e+47
# scaled difficulty: 228.99, suggest sieving rational side
type: snfs
size: 212
skew: 72.9989
c5: 1
c0: -8003480504624389
Y1: -1
Y0: 2562971107509130104661660981719822340812961
m: 2562971107509130104661660981719822340812961

nfs: guessing snfs difficulty 201 is roughly equal to gnfs difficulty 142
nfs: guessing snfs difficulty 206 is roughly equal to gnfs difficulty 145
nfs: guessing snfs difficulty 212 is roughly equal to gnfs difficulty 148

test: generating factor bases
test: fb generation took 3.7376 seconds
test: commencing test sieving of polynomial 0 on the rational side over range 15200000-15202000
gnfs-lasieve4I14e (with asm64): L1_BITS=15, SVN $Revision: 399 $
FBsize 983565+0 (deg 6), 982775+0 (deg 1)
total yield: 3310, q=15202007 (0.04384 sec/rel)
111 Special q, 812 reduction iterations
reports: 27273789->3318298->3054900->1418942->752111->470015
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 3310
0/0 mpqs failures, 2517/1665 vain mpqs
milliseconds total: Sieve 77190 Sched 0 medsched 21020
TD 14620 (Init 560, MPQS 1090) Sieve-Change 32290
TD side 0: init/small/medium/large/search: 1210 1630 770 2600 1160
sieve: init/small/medium/large/search: 1150 10570 830 24810 1360
TD side 1: init/small/medium/large/search: 1350 720 790 2140 520
sieve: init/small/medium/large/search: 1080 11250 790 24880 470
test: new best score of 0.044065 sec/rel
test: estimated total sieving time = 1 day 16h 12m 27s (with 8 threads)

test: generating factor bases
test: fb generation took 2.3693 seconds
test: commencing test sieving of polynomial 1 on the rational side over range 17000000-17002000
gnfs-lasieve4I14e (with asm64): L1_BITS=15, SVN $Revision: 399 $
FBsize 1092015+0 (deg 5), 1091312+0 (deg 1)
total yield: 2318, q=17002019 (0.07025 sec/rel)
121 Special q, 954 reduction iterations
reports: 78196200->1925576->1796836->1268332->668375->370455
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 2318
0/0 mpqs failures, 1583/1334 vain mpqs
milliseconds total: Sieve 85640 Sched 0 medsched 23830
TD 14030 (Init 260, MPQS 860) Sieve-Change 39350
TD side 0: init/small/medium/large/search: 1490 1240 940 2550 850
sieve: init/small/medium/large/search: 870 10750 900 27140 1870
TD side 1: init/small/medium/large/search: 1470 680 870 2170 610
sieve: init/small/medium/large/search: 1030 12640 910 29000 530
test: score was 0.070589 sec/rel
test: estimated total sieving time = 2 days 16h 24m 36s (with 8 threads)

test: generating factor bases
test: fb generation took 2.5353 seconds
test: commencing test sieving of polynomial 2 on the rational side over range 19400000-19402000
gnfs-lasieve4I14e (with asm64): L1_BITS=15, SVN $Revision: 399 $
FBsize 1235031+0 (deg 5), 1234871+0 (deg 1)
total yield: 70, q=19400599 (0.62343 sec/rel) ^Ctest: score was 1.197563 sec/rel
test: estimated total sieving time = 97 days 4h 13m 49s (with 8 threads)
test: test sieving took 364.83 seconds

gen: ========================================================
gen: selected polynomial:
gen: ========================================================

n: 69079449490363446854439633539090428991336131510425369056910132332114073621586198153254665765204271322864118865558921045141352374199158017668202766326392181111307829264122059994138946854180061
# 200029^37-1, difficulty: 201.44, anorm: -3.20e+33, rnorm: 1.77e+38
# scaled difficulty: 207.53, suggest sieving rational side
type: snfs
size: 201
skew: 0.1308
c6: 200029
c0: -1
Y1: -1
Y0: 64055700187902664393213973623321
m: 64055700187902664393213973623321

nfs: guessing snfs difficulty 201 is roughly equal to gnfs difficulty 142
nfs: commencing rational side lattice sieving over range: 7635000 - 7640000
nfs: commencing rational side lattice sieving over range: 7625000 - 7630000
nfs: commencing rational side lattice sieving over range: 7605000 - 7610000
nfs: commencing rational side lattice sieving over range: 7610000 - 7615000
nfs: commencing rational side lattice sieving over range: 7600000 - 7605000
nfs: commencing rational side lattice sieving over range: 7620000 - 7625000
nfs: commencing rational side lattice sieving over range: 7615000 - 7620000
nfs: commencing rational side lattice sieving over range: 7630000 - 7635000[/code]

Currently I think I can only find a list of roadblocks that when cleared would simplify the proof for >=1600.
Is there a list anywhere of composites the if factored would allow a proof to n digits? wblipp's page has this list for a BCR proof but I can't see one on pascals page providing that info.
I assume there would be different lists for total number of prime factors and largest component.

edit: How were the initial factors to forbid chosen? Was it just experimentation?