forstep(x=2*n+1,sqrt(2^n-1),[2*n],if(isprime(x),if((2^n-1)%x==0,print(2"^"n"-1 isn't prime")));break()) an attempt at a Mersenne trial factor code that doesn't work as intended, with a forprime loop around the code it only captures 11 23 and 83 between 2 and 100. anyone for help ?

[QUOTE=axn]Some large Trial Division records: [url]http://primes.utm.edu/top20/page.php?id=18[/url]
[/QUOTE]

I mentioned Generalized Fermat divisors. They do not count as trial division, as only *one* division took place, and there was no division of successive primes up to the divisor.

Trial division --> Successive divisions taking place with increasing odd or prime numbers in order to find a factor, usually starting from 3 (Unless the number is even), until a factor is found or until the number is proven prime.

Under the [B]correct[/B] definition, GFN divisors do not count as trial factoring/trial division records.

[URL="http://en.wikipedia.org/wiki/Trial_division"]Here you go[/URL].

[QUOTE=science_man_88]definition*/definitions*
[/QUOTE]

I was in the middle of editing!

[QUOTE=3.14159;223299]I was in the middle of editing![/QUOTE]

sorry it was up already and do you have any helpful advice for my Mersenne trial factor code ?

figured it out though I'd like to change one thing I have to figure out.

[CODE]mtrial(n) = if(isprime(n),forstep(x=2*n+1,sqrt(2^n-1),[2*n],if(isprime(x),if((2^n-1)%x==0,print(2"^"n"-1 isn't prime");break()))))[/CODE]

During the course of the internet timing out (Took 4 hours for it to restart), I found these:
34575 * 2^24350 + 1 (7335 digits)
39469 * 2^24350 + 1 (7335 digits)
18013 * 2^29480 + 1 (8879 digits)
8197 * 2^32950 + 1 (9923 digits)
3201 * 2^61280 + 1 (18451 digits)
12400 * 7^16800 + 1 (14202 digits)
10928 * 6^7560 + 1 (5887 digits)
9940 * 1999^5288 + 1 (17459 digits)
7033 * 2^43210 + 1 (13012 digits)
1696 * 26^12560 + 1 (17776 digits)
26175 * 2^85751 + 1 (25818 digits)
30591 * 20^9260 + 1 (12053 digits)

[QUOTE=science_man_88]sorry it was up already and do you have any helpful advice for my Mersenne trial factor code ?[/QUOTE]

Recommendation: Work with GIMPS. Trial factoring on Mersenne numbers is done there as well.

[QUOTE=3.14159;223296]Under the [B]correct[/B] definition, GFN divisors do not count as trial factoring/trial division records.[/QUOTE]

Does the trial factoring done by GIMPS for mersenne numbers count as trial division?

[CODE]mtrial(n) = forstep(x=2*n+1,sqrt(2^n-1),[2*n],if(isprime(x),if((2^n-1)%x==0,print(2"^"n"-1 isn't prime");break())))[/CODE]

more up to date version.

[QUOTE=axn]Does the trial factoring done by GIMPS for mersenne numbers count as trial division?
[/QUOTE]

Yes.

[CODE]
(08:39) gp > factor(2^11-1)
%28 =
[23 1]

[89 1]

(09:45) gp > factor(2^23-1)
%29 =
[47 1]

[178481 1]

(09:45) gp > floor(178481/23)
%30 = 7760
(09:45) gp > %/8
%31 = 970
(09:45) gp > factor(2^29-1)
%32 =
[233 1]

[1103 1]

[2089 1]

(09:46) gp > floor(1103/29)
%33 = 38
(09:46) gp > floor(2089/29)
%34 = 72
(09:46) gp > %/8
%35 = 9
(09:47) gp > floor(233/29)
%36 = 8
(09:47) gp > factor(2^37-1)
%37 =
[223 1]

[616318177 1]

(09:48) gp > floor(223/37)
%38 = 6
(09:49) gp > floor(616318177/37)
%39 = 16657248
(09:49) gp > %/8
%40 = 2082156
(09:49) gp > mtrial(n) = forstep(x=2*n+1,sqrt(2^n-1),[2*n],if(isprime(x),if((2^n-1)%x==0,print(2"^"n"-1 isn't prime");break())))
%41 = (n)->forstep(x=2*n+1,sqrt(2^n-1),[2*n],if(isprime(x),if((2^n-1)%x==0,print(2"^"n"-1 isn't prime");break())))
(09:49) gp > factor(2^41-1)
%42 =
[13367 1]

[164511353 1]

(09:50) gp > floor(13367/41)
%43 = 326
(09:51) gp > %/8
%44 = 163/4
(09:51) gp > floor(164511353/41)
%45 = 4012472
(09:51) gp > %/8
%46 = 501559
(09:51) gp > factor(2^43-1)
%47 =
[431 1]

[9719 1]

[2099863 1]

(09:55) gp > floor(431/43)
%48 = 10
(09:55) gp > floor(9719/43)
%49 = 226
(09:55) gp > %/8
%50 = 113/4
(09:56) gp > floor(2099863/43)
%51 = 48834
(09:56) gp > %/8
%52 = 24417/4
(09:56) gp > factor(2^47-1)
%53 =
[2351 1]

[4513 1]

[13264529 1]

(09:57) gp > floor(2351/47)
%54 = 50
(09:57) gp > floor(4513/47)
%55 = 96
(09:57) gp > %/8
%56 = 12
(09:57) gp > floor(13264529/47)
%57 = 282224
(09:57) gp > %/8
%58 = 35278
(09:57) gp > factor(2^53-1)
%59 =
[6361 1]

[69431 1]

[20394401 1]

(09:58) gp > floor(6361/53)
%60 = 120
(09:58) gp > %/8
%61 = 15
(09:58) gp > floor(69431/53)
%62 = 1310
(09:59) gp > %/8
%63 = 655/4
(09:59) gp > floor(20394401/53)
%64 = 384800
(09:59) gp > %/8
%65 = 48100
(09:59) gp > factor(2^59-1)
%66 =
[179951 1]

[3203431780337 1]

(10:01) gp > floor(179951/59)
%67 = 3050
(10:01) gp > %/8
%68 = 1525/4
(10:01) gp > floor(3203431780337/59)
%69 = 54295453904
(10:01) gp > %/8
%70 = 6786931738
(10:01) gp > factor(2^67-1)
%71 =
[193707721 1]

[761838257287 1]

(10:03) gp > floor(193707721/67)
%72 = 2891160
(10:04) gp > %/8
%73 = 361395
(10:04) gp > floor(761838257287/67)
%74 = 11370720258
(10:04) gp > %/8
%75 = 5685360129/4
(10:04) gp > factor(2^71-1)
%76 =
[228479 1]

[48544121 1]

[212885833 1]

(10:06) gp > floor(228479/71)
%77 = 3218
(10:06) gp > %/8
%78 = 1609/4
(10:06) gp > floor(48544121/71)
%79 = 683720
(10:07) gp > %/8
%80 = 85465
(10:07) gp > floor(212885833/71)
%81 = 2998392
(10:07) gp > %/8
%82 = 374799
(10:07) gp > floor(212885833/71)[/CODE]

most of these have a factor that floor(factor/exponent)%8==0 I think I can fit the exceptions to my thinking into a hypothesis but then it would likely be ruined by the law of small numbers.

oh and I just tried it for exponent 1531 and it worked towards what I am now thinking.

next exception of always having at least one factor that floor(factor/exponent)%8==0 is 79. but I can use a different phrasing to include this exception.

Instead of
[code]floor(178481/23)[/code]
try
[code]178481[COLOR="Red"]\[/COLOR]23[/code]

[QUOTE=CRGreathouse;223351]Instead of
[code]floor(178481/23)[/code]
try
[code]178481[COLOR="Red"]\[/COLOR]23[/code][/QUOTE]

thanks for the tip.

137 is the next number that goes by 67's rules.