fond of a factor? Urn yourself to become remains - Page 31

alpertron · 2012-04-20, 14:17

Today my computer found a 132-bit prime:

[Fri Apr 20 08:12:57 2012]
P-1 found a factor in stage #1, B1=10000000.
M798257 has a factor: 4593821825255405094261984523461159901759
k = 3 × 83 × 149 × 1163 × 1223 × 16561 × 794033 × 1425649 × 2908519

I'm running B1 = 10M, B2 = 200M for all numbers in the range 790K to 800K and this is the 7th prime found so far.

Brain · 2012-04-20, 16:07

Quote:

Originally Posted by Brain

How could I miss that... Sorry. Beat this!

Quote:

Originally Posted by alpertron

Today my computer found a 132-bit prime:

[Fri Apr 20 08:12:57 2012]
P-1 found a factor in stage #1, B1=10000000.
M798257 has a factor: 4593821825255405094261984523461159901759
k = 3 × 83 × 149 × 1163 × 1223 × 16561 × 794033 × 1425649 × 2908519

I'm running B1 = 10M, B2 = 200M for all numbers in the range 790K to 800K and this is the 7th prime found so far.

It is prime. So, we have a new thread local record... Congrats!

c10ck3r · 2012-04-23, 23:43

Found a notable one starting out my 84M run...
M84004787 has a factor: 12824399621243547529430624238490771516609
k=2 ^ 5 x 3 x 313 x 4657 x 545482978807033815692147
Factors were-130229148576592177313 and 98475646669079490593, both found while taking to 67 bits. XD

ckdo · 2012-04-24, 06:40

Quote:

Originally Posted by c10ck3r

Found a notable one starting out my 84M run...
M84004787 has a factor: 12824399621243547529430624238490771516609
k=2 ^ 5 x 3 x 313 x 4657 x 545482978807033815692147
Factors were-130229148576592177313 and 98475646669079490593, both found while taking to 67 bits. XD

The notable part is that your misunderstanding of the "k" concept.

cheesehead · 2012-04-24, 07:21

Quote:

Originally Posted by c10ck3r

Found a notable one starting out my 84M run...
M84004787 has a factor: 12824399621243547529430624238490771516609
< snip >
Factors were-130229148576592177313

k = 2⁴ × 48445583143

Quote:

and 98475646669079490593

k = 2⁴ × 36633197563

Quote:

Originally Posted by ckdo

The notable part is that your misunderstanding of the "k" concept.

But 12824399621243547529430624238490771516609 = 2 × (2⁵×3×313×4657×545482978807033815692147) × 84004787 + 1, so that k does have meaning, too. Even though composite, this factor is of the form 2kp + 1.

(Now, that last k should not be compared to either of the preceding k's on some equal basis, because it's algebraically derivable from them, as Dubslow shows below.)

Dubslow · 2012-04-24, 07:31

$(2kp+1)*(2mp+1) = 4(km)(p^2)+2p(m+k)+1 = 2(2kmp+m+k)p+1 = 2(m[2kp+1]+k)p+1 = 2(k[2mp+1]+m)p+1$
[/sm88]

LaurV · 2012-04-24, 07:40

The guy made a joke (he is the joker, remember? see his id is "ciocker") and you all jumped to ~~kill~~ adnotate (@cheesehead:

) him, first of you saying nonsense, the second of you forgetting duplicated phrases in the text, and the third losing a "p" on the way in that calculus, hehe, THAT is really funny

And by the way, you don't need to close the \tex box to write subscripts and superscripts... $x_1^2+x^3_4=x^{2^3}_{1_4}$

cheesehead · 2012-04-24, 07:45

Quote:

Originally Posted by LaurV

The guy made a joke (he is the joker, remember? see his id is "ciocker") and you all jumped to kill him,

"kill" ???

How about "annotate" ?

LaurV · 2012-04-24, 07:55

Now it looks much better, last 3 posts could be deleted (my two including this one, and cheesehead's one in between). Well, we lose the fun, but the thread would be clearer. Or well... the thread would be clearer, but we will lose the fun...

Dubslow · 2012-04-24, 08:04

Quote:

Originally Posted by LaurV

Now it looks much better, last 3 posts could be deleted (my two including this one, and cheesehead's one in between). Well, we lose the fun, but the thread would be clearer. Or well... the thread would be clearer, but we will lose the fun...

Since when was clarity ever our first goal?

(Shows how little Tex I know :P)

Batalov · 2012-04-24, 08:16

(easy warm-up) M1091 has a prime factor 2·k·1091+1, where

Code:

k = 179 · 69737 · 4086974693 · 7727500822367 · 10227820166017 · 196164761709907 · 8326159283085775335016522402181511923674994349944795840347158060798548700472189268029761648871175757465278359531733261197555258091948229635309347779196749685783

M10169 has a prime factor 2·k·10169+1, where

Code:

k = 2^4 · 3^3 · 11 · 18196183 · 967157656641434911 · 8437886386...17_<2988>

2012-04-20, 14:17	#331
alpertron Aug 2002 Buenos Aires, Argentina 2·683 Posts	Today my computer found a 132-bit prime: [Fri Apr 20 08:12:57 2012] P-1 found a factor in stage #1, B1=10000000. M798257 has a factor: 4593821825255405094261984523461159901759 k = 3 × 83 × 149 × 1163 × 1223 × 16561 × 794033 × 1425649 × 2908519 I'm running B1 = 10M, B2 = 200M for all numbers in the range 790K to 800K and this is the 7th prime found so far. Last fiddled with by alpertron on 2012-04-20 at 14:20

2012-04-24, 07:31	#336
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 16065₈ Posts	$(2kp+1)(2mp+1) = 4(km)(p^2)+2p(m+k)+1 = 2(2kmp+m+k)p+1 = 2(m[2kp+1]+k)p+1 = 2(k[2mp+1]+m)p+1$ [/sm88] Last fiddled with by Dubslow on 2012-04-24 at 08:05 Reason: cheating :P*

2012-04-24, 07:40	#337
LaurV Romulan Interpreter Jun 2011 Thailand 9656₁₀ Posts	The guy made a joke (he is the joker, remember? see his id is "ciocker") and you all jumped to ~~kill~~ adnotate (@cheesehead: ) him, first of you saying nonsense, the second of you forgetting duplicated phrases in the text, and the third losing a "p" on the way in that calculus, hehe, THAT is really funny And by the way, you don't need to close the \tex box to write subscripts and superscripts... $x_1^2+x^3_4=x^{2^3}_{1_4}$ Last fiddled with by LaurV on 2012-04-24 at 07:56

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2012-04-23, 23:43	#333
c10ck3r Aug 2010 Kansas 547 Posts	Found a notable one starting out my 84M run... M84004787 has a factor: 12824399621243547529430624238490771516609 k=2 ^ 5 x 3 x 313 x 4657 x 545482978807033815692147 Factors were-130229148576592177313 and 98475646669079490593, both found while taking to 67 bits. XD

2012-04-24, 07:55	#339
LaurV Romulan Interpreter Jun 2011 Thailand 2³·17·71 Posts	Now it looks much better, last 3 posts could be deleted (my two including this one, and cheesehead's one in between). Well, we lose the fun, but the thread would be clearer. Or well... the thread would be clearer, but we will lose the fun...