Prime95 - suggest using B2 bound = GMP-ECM default and other questions

[GP2]

Originally Posted by Raman

Still wondering how that extremely smooth ECM curve prime factor or ECM curve prime number had been found out.
[...]

I doubt that if it were really found out by using ECM curves!
Neither Prime95 ECM curves nor GMP-ECM ECM curves would have been able to be found it out. Right?

If you google the number 493613348917766417426006591803225943649556875046256846631045789294232301761, you find this old thread: "Faking factors with Complex Multiplication", and within that thread post #4 discusses that number. It does seem it was found artificially, if I understand that post correctly.

Originally Posted by Raman

Windows version of Prime95 does not use up with the PRP tests for the type of the work outs to be assigned with the select option from the combo box at all. Right?
They need to be only manually entered from the worktodo.txt file or what? Linux / Unix version of mprime only accepts with the inputs from worktodo.txt file manually entered or automatically assigned. Do they not have with the graphical user interface or the menu styles for the type of the work outs to be assigned with the select option from the combo box? They are only menu styles!

Primenet doesn't assign PRP tests or accept PRP test results. Prime95 can do PRP testing, but it can't be selected from any menus, you have to manually add lines to a worktodo.txt file. But you have to be careful, because any PRP results you obtain have to be manually reported to mersenne.ca (NOT mersenne.org) by copying and pasting the lines from results.txt, otherwise those results will be lost.

You can obtain PRP assignments from mersenne.ca at this page at mersenne.ca by clicking on a link in the rightmost "Assignments" column. Those pages don't really give any instructions, which is unfortunate.

[GP2]

Originally Posted by axn

GMP-ECM uses a completely different stage 2 algorithm from P95 (something like O(sqrt(B2)) vs O(B2)). It is hugely (yuugely!) more memory-intensive, but can attain much higher B2 in the same time.

I think GMP-ECM can only be used on rather small exponents. What is the limit in practice for the largest exponents that you would attempt with GMP-ECM?

[lycorn]

Sometime ago I ran a couple of curves on different exponents and B1/B2 bounds and came to the conclusion that using Prime95 for Stage 1 and GMP-ECM for Stage 2 pays for exponents up to ~40K, but the smaller the exponent the more significant the gains are.
I´m still using that combo for very small exponents (1277, for one). May be Santa will drop something down my chimney, who knows?...

[Raman]

Originally Posted by Raman

Order Sorted Up

Away out off up down my own. Of with that that this is always existing out!
My own.
Away out off up down. Of with that that this is always existing out!

77. 2¹⁷²⁷⁵⁹-1 has a factor: 672002676922157179283240771609
Fingers crossed up - keep up stay away...!

Originally Posted by Raman

Tension = Stress?
Ratio ration approximation factor rate - where ever as like!
Of for from front frontier - of of just that is being - rather than instead of - in to the before wards after wards to wards over there by - of with but that that - of that which that this!

Good enough in to the have got been results per month statistics!
Good enough in to the have got been Mersenne prime number exponents per 1000000 statistics - of the following form - where ever as like!
Good enough in to the have got been age per days statistics!

[Raman]

78. 2^1408087-1 has a factor: 2138342186768010337729.

[Raman]

Interesting to ask up with:

always

If I run away 5 ECM curves for each Mersenne number with no known prime factors exponents
between 600000 and 700000 with B1 = 250000 and B2 = 128992510

and

if TJOAI runs away 25 ECM curves for each Mersenne number with no known prime factors exponents
between 600000 and 700000 with B1 = 50000 and B2 = 5000000

then

what will be the chance that he would find out the same prime factor before wards of me doing
it extracting up?

For the factors of any size - at all - small or medium or large - any way some how every day

[Raman]

Suppose that if I run a lot of ECM curves stage 1 only up on say (2⁵²⁴²⁸⁷+1)/3 with B1 = 11000000 and store away their own same hexadecimal residues in to a text editor file case. With GMP-ECM or Prime95 will I be able to continue away with stage 1 only with those same their own stored away hexadecimal residues with B1 = 44000000 with those in to a text editor file case?

Originally Posted by Raman

M1277 is that next Mersenne number with no known factors at all, after that only M1619.
M1277 I guess that it may have a much larger enough prime factor, as it is closer to
that prime number: M1279. Similarly as it was that case for M521, which is prime,
M523 has a prime factor, that splits up into p69.p90

Why at Mersenne.org Exponent status web site page, query results are being limited to 1000 exponents?

Originally Posted by Raman

By the way, why did Prime Net Server once assign one of single systems and then computers or machines for Trial Factoring assignment
when I was looking out only for ECM curves on to smaller Mersenne composite numbers assignment?

A single of NF line, strangely and unusually sandwiched between a lot of F-ECM lines.

CPU Name: Karpov Michael Raj K.
Exponent: 135062611
Result Type: NF
Received: 2016-09-23 06:51
Age Days: 1.7
Result: no factor from 2⁷⁰ to 2⁷¹
GHz-Days: 1.7705

Originally Posted by Raman

Please define what do you mean by semi-prime. I have heard of prime, but not semi-prime
at all. Do you mean that it has got only two prime factors, with it actually?

If so, M1063 & M881 are being semi-primes, as well, as is being the case for M523, M809, M727,
M971, M983, M997.

And then, I will define my own terms, as well. I will call 2*prime, a fraud prime, for
this example, consider taking away with 3⁵⁴¹-1,

and then 5*prime, a cheat prime, 6²⁷¹-1, as since 2 & 5 are alone being the
trivial prime factors to be making the number composite, alone.

Already in its own best place,
at Mersenne.org ECM progress web site page not in its own synchronization with at Mersenne.org Exponent status web site page.

Originally Posted by Raman

ECM on numbers like 2¹²⁷⁷-1, 2¹⁶¹⁹-1, 2¹⁷⁵³-1, 2²¹³⁷-1, 2²²⁶⁷-1, 2²²⁷³-1, 2²³⁵⁷-1, 2²³⁷⁷-1, 2²⁴²³-1, 2²⁴⁷⁷-1, 2²⁵²¹-1, 2²⁵⁵⁷-1, 2²⁶⁷¹-1, 2²⁷¹³-1, 2²⁷¹⁹-1, 2²⁸⁵¹-1, 2³⁰⁴⁹-1, etc.
will probably be totally futile without producing any useful results.

Prime numbers p below 10000 such that 2^p-1 is composite but has got no known prime factors.
p ≤ 10000.

1277, 1619, 1753, 2137, 2267, 2273, 2357, 2377, 2423, 2477, 2521, 2557, 2671, 2713, 2719, 2851, 3049, 3673, 3691, 3847, 3881, 3919, 4007, 4049, 4111, 4159, 4261, 4363, 4567, 4583, 4591, 4703, 4721, 5443, 5471, 5503, 5839, 6007, 6073, 6247, 6581, 6679, 6733, 6763, 6971, 7069, 7127, 7321, 7351, 7621, 8291, 8329, 8369, 8389, 8581, 8681, 8923, 8999, 9011, 9227, 9463, 9473, 9551, 9679, 9857, 9929.

Much more larger prime factors are only being known recently, after wards when ever the Prime Net web site page server and client went automated after wards when ever.

1061: 46817226351072265620777670675006972301618979214252832875068976303839400413682313921168154465151768472420980044715745858522803980473207943564433.
1237: 2538207129840687799335203259492870476186248896616401346500027311795983.
1657: 10788426156438350117334292343137689257142387557947087583.
1669: 112493750443412941745410571996247741731544451845539488817.
2269: 5198395892876421104415109549087087419559080537214372111.
3607: 162160065980366340636967897279169391509046358190713.
4937: 224209400033890009931837488284049711636925260561.
5309: 4379627179880971499877583266262615461322386849281.
5879: 3381116440321017148580653633902983992991015840485797617951.
5923: 39615112643045557727531880705107806493554991.
6211: 1110196860540711188306812523817624319633363099818286801.
6329: 26367627467345446174566335936121340946860202281.
9209: 1821133994357721169773431211508950567060217.
9587: 6842693325161318357698161937504324710196297.

Text automatically adjusts itself to size of device and panel screen width.

Originally Posted by Raman

A good observation...

2¹⁰⁶¹-1 has got a prime factor of size = 143 digits.

1061 = Number of four-digit prime numbers
143 = Number of three-digit prime numbers

If someone were to be
being doing some research along this line, and then
he / she would have certainly guessed it very much easily itself!

In contrast,

Open end aliquot sequences and series below 1000.
Starting element ≤ 1000.
All members.
Of side sequences and series.

276, 306, 396, 696
552, 888
564, 780
660, 828, 996
966

Originally Posted by Raman

I would suggest the 2- table to be extended atleast upto that exponent of 1280. Note that 2,1237- 2,1277- have no factors at all after 2,1061-. The next is only 2,1619-, and that 2,1279- is prime, so that upto exponent 1280 would be fine enough! 1280 = 5.2⁸

521, 523 are twin primes with M521 being prime, M523 has a large prime factor that is already being conquered. So, is the case with these twin primes 1277, 1279? Note that M1279 is a prime number, thus M1277 should have a large enough prime factor?

In contrast,

Open end aliquot sequences and series below 10000.
Starting element ≤ 10000.
Lowest members.
Of side sequences and series.

276, 552, 564, 660, 966, 1074, 1134, 1464, 1476, 1488, 1512, 1560, 1578, 1632, 1734, 1920, 1992, 2232, 2340, 2360, 2484, 2514, 2664, 2712, 2982, 3270, 3366, 3408, 3432, 3564, 3678, 3774, 3876, 3906, 4116, 4224, 4290, 4350, 4380, 4788, 4800, 4842, 5148, 5208, 5250, 5352, 5400, 5448, 5736, 5748, 5778, 6396, 6552, 6680, 6822, 6832, 6984, 7044, 7392, 7560, 7890, 7920, 8040, 8154, 8184, 8288, 8352, 8760, 8844, 8904, 9120, 9282, 9336, 9378, 9436, 9462, 9480, 9588, 9684, 9708, 9852.

Any patterns are being found out as like them?
Any progress in computations will be able to reduce these numbers down as like them they are being.
As like them, they are not being suitable enough for OEIS entries.
As like them, they are being applicable enough for T-shirt or formal shirt design patterns.

import java.lang.*;
import java.io.*;
// import java.util.*;
public class Results
{
public static void main(String args[])
{
try
{
RandomAccessFile file=new RandomAccessFile("results20161017.txt","rw");
RandomAccessFile W8191=new RandomAccessFile("W8191.txt","rw");
RandomAccessFile W19937=new RandomAccessFile("W19937.txt","rw");
RandomAccessFile W110503=new RandomAccessFile("W110503.txt","rw");
RandomAccessFile W524287=new RandomAccessFile("W524287.txt","rw");
// List l=new ArrayList<Integer>();
while(true)
{
String s=file.readLine();
if(s==null)
{
break;
}
else
{
String t=s.trim();
int i=t.length();
// if(!l.contains(i))
// {
// l.add(i);
// }
if(i>=262176&&i<=262179)
{
W524287.writeBytes(t+"\n");
}
else if(i>=55284&&i<=55287)
{
W110503.writeBytes(t+"\n");
}
else if(i>=10001&&i<=10003)
{
W19937.writeBytes(t+"\n");
}
else if(i>=4129&&i<=4131)
{
W8191.writeBytes(t+"\n");
}
}
}
// System.out.println(l);
}
catch(IOException e)
{
System.out.println(e.toString());
}
}
}

My own JAVA package distribution programming language scripting code.

For reading out results from results.txt text editor file case and then sorting them away in to the W8191.txt, W19937.txt, W110503.txt, W524287.txt text editor file case.

Originally Posted by Raman

Hope that they will also be factored off sooner itself!
M521 is prime, M523 had a larger sized factor. M1279 is prime, so that M1277 will thus have much larger enough factor?!

Mersenne Forum does not have colour for formatting code from
my own JAVA package distribution programming language scripting?

Originally Posted by Raman

• Consider with Mersenne Numbers of the following form 2^p-1, there are being plenty of prime numbers of the following form 2kp+1 but only a few of them would divide 2^p-1 such that their own product ≤ 2^p-1. Due to a theorem of Number Theory, a prime number of the following form 2kp+1 should indeed obviously divide with 2^kp-1. So that, 2kp+1 should divide with 2^p-e^nπi/k for a some integer n such that 0 ≤ n ≤ 2k-1. For example, 367 = (2 × 3 × 61) + 1 neither divides with 2⁶¹-1 nor divides with 2⁶¹+1 but it should divide with 2³⁶⁶-1 = (2⁶¹-1) × (2⁶¹+1) × (2¹²²-2⁶¹+1) × (2¹²²+2⁶¹+1). Indeed 367 divides with (2¹²²+2⁶¹+1).
  For k = 1 case, this reduces in to if 2p+1 is being a some prime number for a some prime number p, then it should divide with either 2^p-1 (when 2 is being quadratic residue (mod 2p+1), 2p+1 ≡ 1 or 7 (mod 8)), or divide with 2^p+1 (when 2 is being quadratic non-residue (mod 2p+1), 2p+1 ≡ 3 or 5 (mod 8)). (p that is being Sophie-Germain prime number. 2p+1 is also being prime number too!)

Can zeros of Riemann Zeta Function be able to provide away us with any useful information about prime factors size or their own distribution when ever that it is being possible? Probably perhaps potentially.
Trivial zeros or non-trivial zeros.
Give away us with any productive information or hint or clue.

Originally Posted by Raman

Quite very variably - about around - round ground - poultry variety.
Away out up off down my own - that ever which ever a way a way - ever - by using be being - ever.

Super Computer Words
Order Sorted Up

Away out off up down my own. Of with that that this is always existing out!
My own.
Away out off up down. Of with that that this is always existing out!

Questions and answers mode turning out in to the Report Results mode.
As like turning out in to the.

[Raman]

Interestingly enough.

An ECM curve stage 1 up on (2⁸¹⁹¹+1)/3 with B1 = 3×10⁹ will take up to 19 hours and ECM curves stage 1 up on other three numbers
(2¹⁹⁹³⁷+1)/3 with B1 = 3×10⁸
(2¹¹⁰⁵⁰³+1)/3 with B1 = 5×10⁷
(2⁵²⁴²⁸⁷+1)/3 with B1 = 1.1×10⁷
will take much shorter time.

On a 4 core Core i5 processor.

A few days ago my computer had restarted just after finishing off with an ECM curve stage 1 up on (2⁸¹⁹¹+1)/3 with B1 = 3×10⁹.
Its hexadecimal residue had been just written out to worktodo.ini file.
When the computer restarted, the same hexadecimal residue had been again written out to worktodo.ini file.
I wondered why.
Because the back up file from which Prime95 for Windows or mprime for Linux restarts had been written out just before the same ECM curve had been got finished off with!

Luckily enough, the computer did not restart before the ECM curve had been got finished off with!

Luckily enough, the trivial prime factor of 3 had been written out to the old σ value which had been just got off finished before itself with!
No significant computational efforts wasted out due to this restarting of computer off at all!
In fact it is the case that my above mentioned statement that the same hexadecimal residue had been again written out to worktodo.ini file is false!
In fact that it was the case the old σ value along with the trivial prime factor of 3 had been written out to the worktodo.ini file!

If the computer goes down again, and if I have to re-install with Ubuntu, then it will be better off to back up files in to local git hub server and client repository.
In to the year of 2010, age me 22 years old, I had received up with a Ubuntu CD for free from the Netherlands and the Holland!

It is an obsolete version of Ubuntu operating system off right now!

By using superscript and subscript tags of powers, it is better off rather than instead of by using ^ symbol at all right now!
And ⊕ this is the proper symbol for the XOR operation at all right now!

Any one who downloaded up with my previously attached files running away with Stage 2 of ECM curves off up on their own computers?
Any way that it is the case the I have attached up with the hexadecimal residue file cases for ECM curves of stage 1 off for (2⁸¹⁹¹+1)/3 and (2¹⁹⁹³⁷+1)/3 because they are comparatively smaller enough!
On the other hand, those for (2¹¹⁰⁵⁰³+1)/3 and (2⁵²⁴²⁸⁷+1)/3 but they are comparatively larger enough!

Rather than instead of...

And last but not the least, why do we increment up with group order ECM curves bounds by using equal to 5 digits, why not by using greater than 5 digits or by using lesser than 5 digits?

Equal to symbol - and cord or wire.

No log in ID is required in to the downloading up with attachments at all right now! Isn't it?

Copy and paste is a useful feature, whether cut and paste or copy and paste - common key is Control + V.
Or once in the year of 1997, age me 9 years old, or computer just bought and purchased newly and freshly away.
Control + V was used up with After Dark Screen Saver, my parents were learning Visual Basic 5.0,
Control or Control + Shift was needed up with After Dark Screen Saver, they have been got frustrated up with.
Opened up with Dfields and Cfields rather than instead of later on changed up with Control + W.

Not to touch up with Visual Basic 5.0 then? Why?
Good learning opportunities then!
Opportunities can be grabbed up with only during development phases!

Have been got refuted up with!
Not Not Not.

Visual Basic 6.0 will be taught up with at plus one.
Super Computer bought and purchased up with or - year of 1995 off for - for age me 7 years old - ideal time in to the learning of type writing off for - for.
Raman computer bought and purchased up with or - year of 1997 off for - for age me 9 years old of off for - for.
Venkatesh + Lakshmi computer bought and purchased up with or - year of 2000 off for - for age me 12 years old of off for - for.
Aswini computer bought and purchased up with or - year of 2000 off for - for age me 12 years old of off for - for.
Arvind + Aroona computer bought and purchased up with or - year of 2002 off for - for age me 14 years old of off for - for.

Computer configuration asked up with - electronic configuration!
And up with or - year of 2002 off for - for age me 14 years old of off for - for.

[sweety439]

Originally Posted by Raman

I had to add up on with in a some of these prime factors for in to factordb.com web site page - for only of certainly ≤ 10000000 digits - limit range bound level - rate ratio scale proportion - exists out!

The Wagstaff Mersenne number (2^{170141183460469231731687303715884105727}+1)/3 has a factor: 886407410000361345663448535540258622490179142922169401

See https://www.mersenneforum.org/showthread.php?t=25703

[sweety439]

Conjectures:

* The largest double Mersenne prime is 2^127-1

* The largest Wagstaff Mersenne prime is (2^127+1)/3

* The largest Mersenne Wagstaff prime is 2^3-1

* The largest double Wagstaff prime is (2^43+1)/3

* The largest Mersenne Fermat prime is 2^17-1

* The largest Wagstaff Fermat prime is (2^17+1)/3

Also,

* Phi_{Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 12

* Phi_{2*Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 10, 12, 14

Where Phi is the cyclotomic polynomial

[paulunderwood]

Originally Posted by sweety439

* The largest double Mersenne prime is 2^127-1

What supporting evidence do you have to this conjecture?

Why do you believe MM127 is not prime?

In the sea of infinity what is there to stop a bigger double Mersenne prime existing?