Date: Feb 11, 2013 11:30 AM Author: Subject: Re: SHORT HAND OF PRIME NUMBER DISTRIBUTION CORRECTED FILE On Friday, February 8, 2013 10:12:29 PM UTC, hope...@frontier.com wrote:

Regarding M48 which has recently been added, it is being discussed [http://mersenneforum.org/showthread.php?t=17704 here]. [http://mersenneforum.org/showpost.php?p=326083&postcount=69 Here] it is claimed primality has been verified. -- a prime is 28829407 69 0x849E58408C92DE__ 23-Aug-08 7:41 hagenbuchner XENserv1

32428427 69 0xB6C80137FEDB7E__ 23-Aug-08 7:49 suuuncon SPDELL

36705287 70 0xDDA8BEB967041D__ 23-Aug-08 7:32 dmazh dm2

37425887 68 0x9B10891A72B405__ 23-Aug-08 7:02 BranMuffin ROTV-O4

37763179 70 0xB141C151483C99__ 23-Aug-08 7:34 curtisc wcm128--03L

37946213 69 0x901FF5AA04168E__ 23-Aug-08 7:19 S611352 p4raid

38859463 69 0x5840B65CA7CB7B__ 23-Aug-08 7:23 curtisc JCKL-cce41L

40896127 69 0x4F9CCA10FDF131__ 23-Aug-08 7:35 fcg619 C1391

41935241 69 0xEDB167FA1DBB31__ 23-Aug-08 7:53 S00039 Cinebox_0

41959849 69 0xD689BE98B86C77__ 23-Aug-08 7:53 curtisc grn206--11l

42206137 69 0x0A0EEC17151DAC__ 23-Aug-08 7:33 drrocket MIS5PC

42760397 70 0xA6090C299C0678__ 23-Aug-08 7:46 curtisc JCKL-ccd62L

42781927 69 0x8613884B69237A__ 23-Aug-08 7:56 jmoseley Vader

42796219 69 0x4F4C53A0908A5D__ 23-Aug-08 7:59 DingoDog starfury

42801739 69 0xF6DDB517B9A4C6__ 23-Aug-08 7:44 DingoDog starfury

43096799 69 0x32E28ECEC2C31B__ 23-Aug-08 7:21 TeamRessler 1062315

43112609 69 0x8691696D2BDA50__ 23-Aug-08 7:33 UclaMath C20E3341C

43411699 69 0x7C0112FE295ECD__ 23-Aug-08 7:25 salfter office1535,266,303 (1)MartinMusatov Here goes: If <i>q</i> divides 2<sup><i>p</i></sup> − 1n 2<sup><i>p</i></sup> ≡ 1 (<i>mod</i> <i>q</i>). By [[Fermat's Little Theorem]], 2<sup>(<i>q</i> − 1)</sup> ≡ 1 (<i>mod</i> <i>q</i>). Assume there exists such a <i>p</i> wh@does new divide <i>q</i> − 1. Then as <i>p</i> and <i>q</i> − 1 must be relatively prime, a similar application of Fermat's Little Theorem says @ (<i>q</i> − 1)<sup>(<i>p</i> − 1)</sup> ≡ 1 (<i>mod</i> <i>p</i>). Thus there is a number <i>x</i> ≡ (<i>q</i> − 1)<sup>(<i>p</i> − 2)</sup> for which (<i>q</i> − 1)·<i>x</i> ≡ 1 (<i>mod</i> <i>p</i>), and therefore a number <i>k</i> for wh@ (<i>q</i> − 1)·<i>x</i> − 1 = <i>kp</i>. Since 2<sup>(<i>q</i> − 1)</sup> ≡ 1 (<i>mod</i> <i>q</i>), raising both sides of the congruence to the power <i>x</i> gives 2<sup>(<i>q</i> − 1)<i>x</i></sup> ≡ 1, and since 2<sup><i>p</i></sup> ≡ 1 (<i>mod</i> <i>q</i>), raising both sides of the congruence to the power <i>k</i> gives 2<sup><i>kp</i></sup> ≡ 1. Thus 2<sup>(<i>q</i> − 1)<i>x</i></sup> ÷ 2<sup><i>kp</i></sup> = 2<sup>(<i>q</i> − 1)<i>x</i> − <i>kp</i></sup> ≡ 1 (<i>mod</i> <i>q</i>). But by definition, (<i>q</i> − 1)<i>x</i> − <i>kp</i> = 1, implying that 2<sup>1</sup> ≡ 1 (<i>mod</i> <i>q</i>); in other words, that <i>q</i> divides 1. Thus the initial assumption th@ <i>p</i> does new divide

n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257

Yet the list is as follows:

{| class="wikitable"

|-

! #

! ''p''

! ''M''<sub>''p''</sub>

! Digits in ''M''<sub>''p''</sub>

! Date of discovery

! Discoverer

|-

| align="right" | 8

| align="right" | 31

| align="right" | [[2147483647]]

| align="right" | 10

| 1772

| [[Leonhard Euler|Euler]]

|-

| align="right" | 12

| align="right" | 127

| align="right" | 170141183?884105727

| align="right" | 39

| 1876

| [[Edouard Lucas|Lucas]]

|}

Should not Mersenne be credited for those two?

Alex

[[Special:Contributions/68.46.132.117|68.46.132.117]] ([[User talk:68.46.132.117|talk]]) 05:25, 3 February 2010 (UTC)

No, he merely ''conjectured'' that 2<sup>p</sup>-1 was prime for those values, getting two of his four unproved guesses (for p = 67 and 257) incorrect and missing three more (p = 61, 89 and 109). Euler and Lucas actually ''proved'' that the above two (p = 31 and 127) were prime. The first seven on his list had already been discovered so don't really count. --[[User:Glenn L|Glenn L]] ([[User talk:Glenn L|talk]]) 07:01, 3 February 2010 (UTC)

:Are you sure the first Mersenne primes were discovered by Greeks, and not Mesopotanians, Egyptians, indians or Chinese? and were is the proof (or reference) of this? [[Special:Contributions/192.87.123.159|192.87.123.159]] ([[User talk:192.87.123.159|talk]]) 08:42, 3 May 2010 (UTC)

== (obviously) or 30% of the exponent ==

talk]] ? [[Special:Contributions/MartinGugino|contribs]] </small> 05:10, 27 April 2010 (UTC))

:You're on the right track. More correctly (remember that log<sub>10</sub>2 ? 0.30102999566...):

:Digits<sub>mp</sub> = 1 + int (log<sub>10</sub>2 x p) for Mersenne primes and

:Digits<sub>pn</sub> = 1 + int (log<sub>10</sub>2 x (2p-1)) for perfect numbers. − [[User:Glenn L|Glenn L]] ([[User talk:Glenn L|talk]]) 23:33, 13 August 2010 (UTC)

== A Recently Disproven Mersenne Prime ? ==

Anonymous user 74.3.4.112 noted the following Google Group message:

:An amateur mathematician discovered in early 2010 that Mersenne N86,243 is (divisible by 1,627,710,365,249) and N1,398,269.

:[[Harry Nelson|Nelson]] & [[David Slowinski|Slowinski]] originally discovered thenumber and announced it was prime on September 25, 1982. [http://groups.google.com/group/sci.math/browse_thread/thread/5a1804a03840c3e3# Mersenne Primes Proven Composites?]

However, when I tested M86243 on Prime95, I got: "M86243 is Prime! Wd1: 82145A39,00000000"

Although 1,627,710,365,249 = 86,243 * 18,873,536 + 1 and therefore ''could'' qualify as a factor, I am very suspicious.

-- Glenn L 11:56, 16 May 2010 (UTC)

:The claim was false and has been reverted in [http://en.wikipedia.org/w/index.php?title=Mersenne_prime&diff=362494633&oldid=362385812]. 1,627,710,365,249 is a known factor of 2<sup>86243</sup>+1. The Mersenne prime is 2<sup>86243</sup>?1. [[User:PrimeHunter|PrimeHunter]] ([[User talk:PrimeHunter|talk]]) 00:32, 17 May 2010 (UTC)

If ''p'' is a SG prime and ? 3 (mod 4), 2''p'' + 1 will indeed divide 2^''p'' - 1, but if ''p'' ? 1 this is ''not'' true! 89 is SG and 2^89 - 1 is prime. Hence, the claim in the paragraph cited is in error; you need the stronger fact that there are infinitely many SG primes ? 3 (mod 4).

I added the citation for Euclid's theorem about Mersenne primes and perfect numbers. He phrases it thus: "If as many numbers as we please beginning from an unit be set out continuously Quite some time ago the date for the find of Mersenne prime #30 was changed from "September 20 1983" to "1983 September 19" and for #31 from "September 6 1985" to "1985 September 1" without giving any reliable sources for these changes. So find equal amount of prime numbers and composite numbers "it is the first in which an equal amount of incomposite and composite numbers are seen." The prime numbers (incomposite) referred to here must be 1, 2, 3, 5 and 7. The composite numbers must be 4, 6, 8, 9 and 10. So, the conclusion from this passage is, even if it is an implicit reference, that Philolaus knew that 3 and 7 are prime numbers.<br />

<br />

So the reason why I also want to include these two parts of the quotation:<br />

A. "Ten does have an equal amount /.../ it is the first in which an equal amount of incomposite [i.e. 1,2,3,5,7] and composite [i.e. 4,6,8,9,10] numbers are seen."<br />

B. "seven is a multiple of none"<br />

is that they give a direct reference to the numbers 3 and 7 as prime numbers and its the first time ever they are said to be prime numbers.<br />

[[Special:Contributions/83.216.101.203|83.216.101.203]] ([[User talk:83.216.101.203|talk]]) 09:57, 25 November 2012 (UTC)

:Still meaningless (may be the fault of the translator) and irrelevant. If you want to report the source that 3 and 7 are prime, do so, but not with inappropriate quotes. ? [[User:Arthur Rubin|Arthur Rubin]] [[User talk:Arthur Rubin|(talk)]] 10:09, 25 November 2012 (UTC)

::What is it that you do not understand? Please explain because to me the quotations are clear and the interpretations are clear. Yes and on some points the greek text is clearer, lets take the passage: "prime and incomposite numbers, and secondary and composite numbers". If you read the greek original you clearly see that it means "prime and incomposite numbers ''on one hand'', and secondary and composite numbers ''on the other hand''". What makes it difficult is that the ancient greeks thought about numbers in a different way then we do, so you really have to get into their way of thinking before you can understand what they wrote. [[Special:Contributions/83.216.101.203|83.216.101.203]] ([[User talk:83.216.101.203|talk]]) 11:03, 25 November 2012 (UTC)

:::You can note that the source found that 3 and 7 are prime (although not that they are '''Mersenne''' primes, because that concept didn't exist), without adding quotes which make no sense in English. ? [[User:Arthur Rubin|Arthur Rubin]] [[User talk:Arthur Rubin|(talk)]] 19:29, 25 November 2012 (UTC)

== M48 ==

Regarding M48 which has recently been added, it is being discussed [http://mersenneforum.org/showthread.php?t=17704 here]. [http://mersenneforum.org/showpost.php?p=326083&postcount=69 Here] it is claimed primality has been verified. -- [[User:Toshio Yamaguchi|'''<span style="color:black;">Toshio</span>''']] [[User talk:Toshio Yamaguchi|'''<span style="color:black;">Yamaguchi</span>''']] 11:09, 27 January 2013 (UTC)

It has not yet been added to [http://v5www.mersenne.org/report_milestones/ the milestones list] though. -- [[User:Toshio Yamaguchi|'''<span style="color:black;">Toshio</span>''']] [[User talk:Toshio Yamaguchi|'''<span style="color:black;">Yamaguchi</span>''']] 11:23, 27 January 2013 (UTC)

:Well, I think it's too early to add M48 to this list. It has not been officially verified. [http://mersenneforum.org/showpost.php?p=326083&postcount=69 Here] Prime95 said "Of course, y'all still have to wait for the official verifications." So according to [[WP:NOTCRYSTAL]], I removed M48 from the list. [[User:Chmarkine|Chmarkine]] ([[User talk:Chmarkine|talk]]) 01:39, 28 January 2013 (UTC)

The prime is 28829407 69 0x849E58408C92DE__ 23-Aug-08 7:41 hagenbuchner XENserv1

32428427 69 0xB6C80137FEDB7E__ 23-Aug-08 7:49 suuuncon SPDELL

36705287 70 0xDDA8BEB967041D__ 23-Aug-08 7:32 dmazh dm2

37425887 68 0x9B10891A72B405__ 23-Aug-08 7:02 BranMuffin ROTV-O4

37763179 70 0xB141C151483C99__ 23-Aug-08 7:34 curtisc wcm128--03L

37946213 69 0x901FF5AA04168E__ 23-Aug-08 7:19 S611352 p4raid

38859463 69 0x5840B65CA7CB7B__ 23-Aug-08 7:23 curtisc JCKL-cce41L

40896127 69 0x4F9CCA10FDF131__ 23-Aug-08 7:35 fcg619 C1391

41935241 69 0xEDB167FA1DBB31__ 23-Aug-08 7:53 S00039 Cinebox_0

41959849 69 0xD689BE98B86C77__ 23-Aug-08 7:53 curtisc grn206--11l

42206137 69 0x0A0EEC17151DAC__ 23-Aug-08 7:33 drrocket MIS5PC

42760397 70 0xA6090C299C0678__ 23-Aug-08 7:46 curtisc JCKL-ccd62L

42781927 69 0x8613884B69237A__ 23-Aug-08 7:56 jmoseley Vader

42796219 69 0x4F4C53A0908A5D__ 23-Aug-08 7:59 DingoDog starfury

42801739 69 0xF6DDB517B9A4C6__ 23-Aug-08 7:44 DingoDog starfury

43096799 69 0x32E28ECEC2C31B__ 23-Aug-08 7:21 TeamRessler 1062315

43112609 69 0x8691696D2BDA50__ 23-Aug-08 7:33 UclaMath C20E3341C

43411699 69 0x7C0112FE295ECD__ 23-Aug-08 7:25 salfter office1535,266,303 (1)MartinMusatov>

>

>

> Dear Editor,

>

> The author has recently published papers as shown under references, and one is due on the spiral sets of prime numbers. This short paper is scientific Diaspora to those Scientists in the world, who are astute enough to understand the different beat of the primordial mathematics, and not the usual mantra of elite science, which is askew for 500 years. Please Review the 100 page article in the Rutherford Journal of New Zealand about ?hunting prime number?. We have proven that the quarry is at our feet and to painfully note the massive historical convolution about a simple matter of Prime numbers in western mathematics. Current mathematicians should be ashamed and as Shakespeare puts it ?What?s here? Portrait of a blinking idiot? that is what current mathematics is, boasting of the largest Prime number at the University of Missouri, USA!!!

>

> The short hand of Prime number distribution:

>

> Vinoo Cameron M.D, Hope research, Athens, Wisconsin

>

> E mail: Hope

>

> Abstract: This is a short paper to demonstrate how complacent scientists are and how complacent journals is .This is simple mathematics that mathematicians have botched for 500 years. I honor IJAMR and JAS of all journals to grasp the short hand of Prime number, something mathematics has missed for a 1000 years. This is also made possible by a unique prime number sieve, that is continuous, the denOtter hope research continuous sieve for prime numbers. Whilst the discovery of large prime number does nothing for the understanding of prime numbers, the short hand does. We have presented a short series and if so called mathematicians cannot extend the series mathematically, they should join a historical line of Western mathematicians that convoluted the reality of mathematics on prime numbers for 500 years

>

> Key Words: Prime number distribution, failure of current mathematics.

>

> Introduction : This is by its published manuscript, and does not need a 100 days of review and refereeing , it is simple , it is clear , it is straight forward, its function is curved, called Chan function by us , to honor the Chinese contribution.

>

> The long hand: This is by infinite two spiral cords (every other Prime number), the author will give only a short example, and I believe the mathematicians are capable of figuring out the rest, because it is simple. It also confirms a correct sieve. Kindly review the published references, listed at the end.

>

> Roll of Prime numbers:

>

>

>

> 11,1319,23,29,31,41,43,47,53,59???the two rational cords are

>

>

>

> A 13, 19,29,37,43...

>

>

>

> B. 11, 17,23,31,41?

>

>

>

> (19*13)+ (19*16) =29*19... (29*19)+ (29*18) = (29*37)... (29*37) +. (37*14)= (43*53)>infinite.

>

>

>

> (17*11) +(17*12)=(17* 23)?(17*23)+(23*14)=(23*31)?(23*31)+(31*18)=(31*41)>>Infinite

>

>

>

> Short hand: of above

>

> 13+16=29; 19+18=37; 29+14=43; 37+16=53>.infinite

>

>

>

> 11+12=23?. 17+14=31?23+18 =41?>infinite

>

>

>

>

>

> Conclusion: This is a shortest paper in the history of Current mathematics; it makes for more understanding of mathematics, than the convolution of your George Riemann and the biggest prime number in University of Missouri USA. I am afraid that the western mathematics has led the rest of the world astray by their Spartan attitudes of the last 500 years that has convoluted Mathematics. A big hat does not make big mathematics.

>

>

>

> References

>

> [1] Cameron .V, The disproof and fall of the Riemann?s hypothesis by quadratic base: The correct variable distribution of prime numbers by the clear mathematics of the half-line values (?Chan function?) of prime numbers, International Journal of Applied Mathematical Research, 2 (1) (2013) 103-110.

>

> [2] Cameron V, den Otter T. Prime numbers 2012. Jam Sci 2012; 8(7):329-334]. (ISSN: 1545-1003), http://www.jofamericanscience.org.

>

> [3] Cameron V, Prime number Coordinates and calculus J Am Sci, 2012; 8(10):9-10]. (ISSN: 1545-1003).http://www.jofamericanscience.org

>

>

>

> [4].Prime number19, Vedic Zero and the fall of western mathematics by theorem. International journal of applied mathematical research 2(1) (2013)111-115

>

>

>

>

>

> Acknowledgements

>

> 1. My Lord Jesus Christ, by his special grace to me, specially the teaching of humility and clarity.

>

> 2. Dr. Hong Ma editor of Journal of American science who was humble / decent to me and understood creativity in Science, he is instrumental in giving us confidence.

>

> 3. IJAMR, and Professor B Bathia, for very decent understanding obtuse mathematics in succinct fashion