Author : Spanu Dumitru Viorel
Address : Street Marcu Mihaela Ruxandra no. 5 , 061524 , Bucharest , Romania
Emails : spanuviorel@yahoo.com
spanu_duitruviorel@yahoo.com
dvspanu@yahoo.com
Phones : +40214131107
+40731522216
Work in progress .
Mathematics. History . Biology .
The Third Conjecture.
The conjecture about the prime numbers of Mersenne .
Textul conjecturii poate fi vizualizat pe www.scribd.com as The Third Conjecture sau cautind
www.Spanu__Dumitru__Viorel
1. Numerele prime sunt caramizile elementare ale numerelor .
De la Aristotel si de la primii pitagoreiceni , stim ca principiile care guverneaza numerele sunt “ principiile care guverneaza toate lucrurile “ . Pytagora , Socrates , Anaximandru , Euclid , toti au urmat stagii de initiere ca Mari Preoti in Egiptul Antic , o civilizatie ale carei cunostinte matematice erau cele mai avansate acum 2500 de ani .
( de vazut exact care au fost matematicienii greci care au urmat cursuri de matematica in Egipt . Cartea despre piramide )
- de inserat citate din cartea “Efectul de piramida “ ; citate “ grecii care au studiat in Egipt ; imagini
Ei credeau ca a reflecta asupra Numarului inseamna a reflecta asupra a “ ceea ce este “ .
Citat . Mathematicianul Don Zagier marturisind despre fascinatia pe care o exercita asupra matematicienilor eleganta si complexitatea numerelor prime :
“ Il y a deux faits concernant la distribuition des nombres premiers qui , je l`espere , vous convaicront avec une telle force qu`ils resteront pour toujours graves dans votre coeur .
Le premier , c`est que ce sont des objets a l`interet purement decorative et qui sont de surcroit les plus arbitrares etudies par les mathematicians . Ils poussent parmi les entiers naturels comme des mauvaises herbes paraisant n`obeir a aucune autre loi que celle du hasard . Personne ne peut prevoir ou se trouvera le suivant .
Le deuxieme fait est encore plus etonnant , parce qu`il dit exactement le contraire : les nombres premiers font preuve d`une regularite ahurissante , leur comportament repond a des lois , et ils obbeisent a ces lois avec une precision quasi militaire . “
Ei credeau ca a reflecta asupra Numarului inseamna a reflecta asupra a “ ceea ce este “ .
2 .- ciurul lui Eratostene → spirala lui Ulam
Right down : Erathostene Sieve . Image show resemblance with Ulam`s Spiral .
.
3 . - program asemanator spirala Ulam ( deja scris; audio )
4 . - numerele prime sunt in numar infinit : demonstratia lui Euclid
5.- numerele prime ale lui Mersenne
6.- numerele duble ale lui Mersenne
7. - numerele perfecte ( paragraph : de ce nu exista numere perfecte impare ? Nu stiu ! )
Supercomputerele actuale au descoperit numere perfecte pare pana la termeni de ordinul 1014 , dar nu au descoperit nici macar un singur numar perfect impar .
Orice numar perfect par este un produs format strict din numere prime atunci cind este descompus in ultima esenta ( nici nu se poate altfel ) .
Problema este ca toate aceste descompuneri contin numarul prim par 2 . Cum influenteaza acest numar prim par , adica 2 , formarea numerelor perfecte ? Atunci cind nu il avem pe 2 ca factor de descompunere in factori primi , numerele respective cresc prea repede . 2 este cel mai mic numar prim !
Trebuie sa existe o functie produs in esenta care intotdeauna va creste mult mai rapid decit o functie suma .
Acum , exista o conjectura care va fi demonstrata cindva si care precizeaza cum stam cu numerele perfecte impare . Aceasta conjectura poate fi vazuta pe www.Spanu__Dumitru__Viorel
ca cea de a XI – a conjectura ( The Eleventh Conjecture ) .
8 . - al 45 - lea si al 46-lea numar al lui Mersenne si al 47 numar prim al lui Mersenne ( de analizat ) .
9 . - programul care testeaza ( deja scris )
10 . - contraargument la predictia bazata pe statistica ( in sensul ca numerele prime ale lui Mersenne ar fi intr-un numar limitat ) Nu putem folosi predictia statistica in lumea numerelor prime pentru ca nu exista nici o lege care sa precizeze exact distributia numerelor prime .
Toate formulele indica probabilitati de aparitie a unui numar prim , exact ca in fizica cuantica ( exemplu: conjectura lui Crammer ) .
Intrucit vorbim de probabilitati nu putem spune exact ca un urmator numar prim al lui Mersenne nu va mai apare . (Author: Spanu Dumitru Viorel )( tocmai a fost gasit cel de al 47 –lea numar prim al lui Mersenne . )
45th and 46th Mersenne Primes Found
The new Mersenne primes are 237,156,667 - 1 = 20225440689097733553...21340265022308220927 and 243,112,609 - 1 = 31647026933025592314...80022181166697152511 (where the ellipsis indicates that several million intervening digits have been omitted for conciseness) and have a whopping total of 11,185,272 and 12,978,189 decimal digits, respectively. Both primes therefore are not only the largest known Mersenne primes, but also the largest known primes of any kind.
47th Known Mersenne Prime
Postscript: The prime has now been officially verified and announced to be M42643801, which has 12837064 decimal digits, making it the 46th known Mersenne prime ranked by size, and hence only the second largest. It was found by Norwegian GIMPS participant Odd Magnar Strindmo.]
Al 47 –lea Numar Prim al lui Mersenne nu are proprietatea formulata de Conjectura a III - a .
The 47th prime number of Mersenne hasn`t the property established by the Third Conjecture .
announced to be M42643801
"s1#=",18.66206610834323,"s#=",42243349,"zet!=",28711,"x1!=",5,"q3!=",5,"x!=",28711
"s1#=",18.66418036119159,"s#=",42272072,"zet!=",28723,"x1!=",5,"q3!=",5,"x!=",28723
"s1#=",18.6662938584946,"s#=",42300801,"zet!=",28729,"x1!=",5,"q3!=",5,"x!=",28729
"s1#=",18.6684077770609,"s#=",42329552,"zet!=",28751,"x1!=",5,"q3!=",5,"x!=",28751
"s1#=",18.67052064638104,"s#=",42358305,"zet!=",28753,"x1!=",5,"q3!=",5,"x!=",28753
"s1#=",18.67263276137841,"s#=",42387064,"zet!=",28759,"x1!=",5,"q3!=",5,"x!=",28759
"s1#=",18.67474456306946,"s#=",42415835,"zet!=",28771,"x1!=",5,"q3!=",5,"x!=",28771
"s1#=",18.67685649147431,"s#=",42444624,"zet!=",28789,"x1!=",5,"q3!=",5,"x!=",28789
"s1#=",18.67896751968489,"s#=",42473417,"zet!=",28793,"x1!=",5,"q3!=",5,"x!=",28793
"s1#=",18.68107838124021,"s#=",42502224,"zet!=",28807,"x1!=",5,"q3!=",5,"x!=",28807
"s1#=",18.68318849017241,"s#=",42531037,"zet!=",28813,"x1!=",5,"q3!=",5,"x!=",28813
"s1#=",18.68529770087236,"s#=",42559854,"zet!=",28817,"x1!=",5,"q3!=",5,"x!=",28817
"s1#=",18.68740718442418,"s#=",42588691,"zet!=",28837,"x1!=",5,"q3!=",5,"x!=",28837
"s1#=",18.68951591656795,"s#=",42617534,"zet!=",28843,"x1!=",5,"q3!=",5,"x!=",28843
"s1#=",18.6916246285266,"s#=",42646393,"zet!=",28859,"x1!=",5,"q3!=",5,"x!=",28859
"s1#=",18.69373273573644,"s#=",42675260,"zet!=",28867,"x1!=",5,"q3!=",5,"x!=",28867
"s1#=",18.69583994681762,"s#=",42704131,"zet!=",28871,"x1!=",5,"q3!=",5,"x!=",28871
"s1#=",18.69794655445086,"s#=",42733010,"zet!=",28879,"x1!=",5,"q3!=",5,"x!=",28879
"s1#=",18.70005357950228,"s#=",42761911,"zet!=",28901,"x1!=",5,"q3!=",5,"x!=",28901
"s1#=",18.70216000092559,"s#=",42790820,"zet!=",28909,"x1!=",5,"q3!=",5,"x!=",28909
"s1#=",18.70426611041517,"s#=",42819741,"zet!=",28921,"x1!=",5,"q3!=",5,"x!=",28921
"s1#=",18.70637147139546,"s#=",42848668,"zet!=",28927,"x1!=",5,"q3!=",5,"x!=",28927
"s1#=",18.70847608459615,"s#=",42877601,"zet!=",28933,"x1!=",5,"q3!=",5,"x!=",28933
"s1#=",18.71058067754165,"s#=",42906550,"zet!=",28949,"x1!=",5,"q3!=",5,"x!=",28949
"s1#=",18.71268495917908,"s#=",42935511,"zet!=",28961,"x1!=",5,"q3!=",5,"x!=",28961
"s1#=",18.7147893650887,"s#=",42964490,"zet!=",28979,"x1!=",5,"q3!=",5,"x!=",28979
"s1#=",18.71689476521428,"s#=",42993499,"zet!=",29009,"x1!=",5,"q3!=",5,"x!=",29009
The programm which gives the prime numbers , according to The Second Conjecture
OPEN "d:/merse10.bas" FOR OUTPUT AS #1
OPEN "d:/merse20.bas" FOR OUTPUT AS #2
OPEN "d:/merse30.bas" FOR OUTPUT AS #3
OPEN "d:/merse40.bas" FOR OUTPUT AS #4
OPEN "d:/merse50.bas" FOR OUTPUT AS #5
OPEN "d:/merse60.bas" FOR OUTPUT AS #6
LET q = 100999
LET x! = 1
1 LET x! = x! + 2
PRINT x!
2 IF x! < q THEN
GOTO 3
END IF
IF x! >= q THEN
END
END IF
3 LET y! = 3
IF x! = 3 THEN GOTO 5
4 IF x! MOD y! = 0 THEN
GOTO 6
ELSE
LET y! = y! + 2
END IF
5 IF y! >= x! - 1 THEN
LET zet! = x!
IF y! >= x! - 1 THEN WRITE #1, "zet!=", zet!
GOTO 7
ELSE
END IF
GOTO 4
6 GOTO 1
7 FOR z! = 1 TO zet! STEP 1
GOTO 10
8 LET q2! = x1!
9 NEXT z!
GOTO 4
10 IF z! MOD zet! = 0 AND z! = zet! THEN
LET q1! = zet ^ 1
ELSE
GOTO 9
END IF
IF x! = 3 THEN LET suma1# = s# + q1! + 2 ELSE LET suma1# = s# + q1!
LET s# = suma1#
WRITE #2, "s#=", s#, "suma1#=", suma1#, "zet!=", zet
WRITE #3, "s#=", s#, "z=", z
LET s1# = (s#) ^ (1 / 6)
IF s1# = INT(s1#) THEN WRITE #4, "x!=", x!, "zet!=", zet!, "s#=", s#, "s1#=", s1#, "z=", z
IF s1# = INT(s1#) AND s1# <> 0 THEN
LET q3! = s1#
ELSE
LET q3! = 5
END IF
LET x1! = 1
IF x1! < q3! THEN
LET x1! = 3
END IF
11 IF q3! MOD x1! = 0 THEN
GOTO 13
ELSE
LET x1! = x1! + 2
END IF
IF x1! >= (q3! - 1) AND (s1# = INT(s1#)) THEN
WRITE #5, "q3!=", q3!, "s#=", s#, "s1#=", s1#, "zet!=", zet!, "x1!=", x1!, "x!=", x!
END IF
WRITE #6, "s1#=", s1#, "s#=", s#, "zet!=", zet!, "x1!=", x1!, "q3!=", q3!, "x!=", x!
12 GOTO 11
13 GOTO 8
11.
New Mersenne Prime Conjecture
Noua conjectura a lui Mersenne .
Consider an odd natural number . If two of the following conditions hold, then so does the third:
1. or ,
2. is prime (a Mersenne prime),
3. is prime (a Wagstaff prime).
• Acesta este o alta conjectura care se refera la numerele prime ale lui Mersenne . Este diferita de cea de a treia conjectura . This is another conjecture about the prime numbers of Mersenne . It is different from the Third Conjecture .
• Urmatoarea asertiune este indoielnica .
• Based on the distribution and heuristics of (cf. http://www.utm.edu/research/primes/mersenne/heuristic.html) the known Mersenne and Wagstaff prime exponents, it seems quite likely that there is only a finite number of exponents satisfying the criteria of the new Mersenne conjecture. In fact, it is likely that there will be no
more Mersenne or Wagstaff prime exponents discovered which fit the criteria.
Conjectura New Mersenne Prime Conjecture
este corecta si tine .
The New Mersenne Prime Conjecture it is correct and holds .
Afirmatia : “ it seems quite likely that there is only a finite number of exponents satisfying the criteria of the new Mersenne conjecture. In fact, it is likely that there will be no
more Mersenne or Wagstaff prime exponents discovered which fit the criteria “ este inutila . Nu ne da nici un indiciu veridic .
Inseram tot articolul de pe www.mathworld.wolfram.com referitor la New Mersenne Prime Conjecture .
New Mersenne Prime Conjecture
Dickson states "In a letter to Tanner [L'intermediaire des math., 2, 1895, 317] Lucas stated that Mersenne (1644, 1647) implied that a necessary and sufficient condition that be a prime is that be a prime of one of the forms , , ."
Mersenne's implication has been refuted, but Bateman, Selfridge, and Wagstaff (1989) used the statement as an inspiration for what is now called the new Mersenne conjecture, which can be stated as follows.
Consider an odd natural number . If two of the following conditions hold, then so does the third:
1. or ,
2. is prime (a Mersenne prime),
3. is prime (a Wagstaff prime).
This conjecture has been verified for all primes . Based on the distribution and heuristics of (cf. http://www.utm.edu/research/primes/mersenne/heuristic.html) the known Mersenne and Wagstaff prime exponents, it seems quite likely that there is only a finite number of exponents satisfying the criteria of the new Mersenne conjecture. In fact, it is likely that there will be no
more Mersenne or Wagstaff prime exponents discovered which fit the criteria. The new Mersenne conjecture may therefore simply be another instance of Guy's strong law of small numbers. In fact, R. D. Silverman (2005) has stated he was present when the conjecture was first posed and quotes Selfridge himself as describing the conjecture as a minor curious coincidence.
SEE ALSO: Catalan-Mersenne Number, Cunningham Number, Double Mersenne Number, Fermat-Lucas Number, Integer Sequence Primes, Lucas-Lehmer Test, Mersenne Prime, Perfect Number, Wagstaff Prime
Portions of this entry contributed by Ernst Mayer
Portions of this entry contributed by John Renze
REFERENCES:
Bateman, P. T.; Selfridge, J. L.; and Wagstaff, S. S. "The New Mersenne Conjecture." Amer. Math. Monthly 96, 125-128, 1989.
Caldwell, C. "The New Mersenne Prime Conjecture." http://primes.utm.edu/mersenne/NewMersenneConjecture.html.
Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, p. 28, 2005.
Silverman, R. D. Post to mersenneforum.org. Apr. 21, 2005. http://www.mersenneforum.org/showpost.php?p=53533&postcount=3.
CITE THIS AS:
Mayer, Ernst; Renze, John; and Weisstein, Eric W. "New Mersenne Prime Conjecture." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NewMersennePrimeConjecture.html
Up . Ulam`s spiral . Prime numbers - the white dots . The more divisors a number has , the bigger is in image .
Spirala lui Ulam : serching for patternss in chaos .
(Down : wonderful picture : “ Pattersns in chaos “ , Kerrie Warren .
Erathostene ( 300 BC )
Leonard Euler : Numerele prime sunt un mister pe care oamenii nu-l vor patrunde niciodata .
Dar vor visa sa-l inteleaga cindva , vor visa cu ochii deschisi .
Ca atunci cind privesti un minunat tablou :” Day dreaming “ , Jo Tunmer .
Tuthankamon , masca mortuara
Egypt, Cairo, Antiquity museum, the gold mask of Tutankhamon
Tutankhamon lived over 3 300 years ago during the period known as the New Kingdom. For two centuries, Egypt had ruled as a world superpower, while its Royal family lived the opulent lifestyle. The powerful priesthood of the god Amon had controlled vast temples and estates.
Peste 700 de ani , cunostintele matematice atit de avansate ale Egiptului Antic , erau transmise talentatilor matematicieni greci care venisera sa invete in tara Nilului .
Piramida egipteana . Coloana din Egipt cu hieroglife inscriptionate .
Coloana din Egipt cu hieroglife inscriptionate .
PIRAMIDELE DIN GIZEH
Intrarea in piramida lui Kefren din Giza , Egipt . Mormintul lui Ramses al III -lea
40 de grade celsius - temperatura
Culoar in piramida . Piramida lui Keops Inregistrare video a mormintului lui Ramses IX.
Piramidele si Sfinxul - Giza / Egipt
Secretele piramidelor
Secretele piramidelor
Anaximandru ( 610 BC – c. 546 BC ) , profesorul lui Pythagora si al lui Anaximenes .
Detail of Raphael's painting The School of Athens, 1510–1511. This could be a representation of Anaximander leaning towards Pythagoras on his left.[ Detaliu din picture lui Rafael , Scoala de la Atena , 1510 – 1511 .
Illustration of Anaximander's models of the universe. On the left, daytime in summer; on the right, nighttime in winter.
Uluitoare reprezentare a Terrei si a corpurilor ceresti apropiate ( chiar daca Geocentrista ! ) , acum aproape 2500 de ani , datorata lui Anaximandru . Cunostintele de astronomie solicita o buna cunoastere a matematicii .
Arhimede (287 -212 BC ) , a fost educat in Egipt de discipolii lui Euclid .
Herodot a fost in Egipt .
Hermes Trismegistos :
. Pithagora ( 580 – 500 BC ) a calatorit in Egipt , unde a ramas 22 de ani si a fost initiat ca Mare Preot .
Thales din Milet :
Teoria “ apei vietii “ pe care Thales o adusese din Egipt . Sa luam , mai intii , literal , aceste afirmatii . “ Apa este principiul fundamental al tututror lucrurilor , din care s-au format toate … ; … s-au format continuu si in care toate se reintorc . Transformarea lucrurilor rezulta din comprimare si diluare . “ Sa presupunem ca Thales nu se referea la apa terestra , ci la spatiu . Ceea ce rezulta , daca inlocuim cuvintul “ apa “ prin “ spatiu “ este extrem de incitant :
“ Spatiul este principiul fundamental al tuturor lucrurilor , din care au aparut toate , s-au creat continuu si in care toate se reintorc . Transformarea lucrurilor rezulta din comprimarea si diluarea spatiului .
( Citat din “ Puterea vindecatoare a piramidelor “ , Manfred Dimde )
Thales a fost initiat in Egipt in matematica , geometrie si astronomie . El a prevazut regelui Cresus o eclipsa de soare pe care o calculase , era in masura sa fixeze sisteme egiptene de masurat , sa calculeze inaltimea piramidelor ,sa puna la punct mijloace pentru indiguirea riului Haly , si sa determine cu exactitate anul de 365 de zile .
In egipt .
Solon anul nasterii : 640 BC in Egipt: 584 BC anul mortii : 559 BC
Anaximandru 611 BC 550 BC 547 BC
( invatacel al lui Thales )
Thales 640 BC 610 BC 543 BC
Pitagora - Profesorul formelor Pi - a stat in egipt din 562 BC pina in 540 BC , in total 22 de ani . El a parcurs acolo stadiile complete pentru preotia egipteana , care dura chiar 22 de ani , si s-a intors in Grecia , dupa ce a stat 12 ani si in Mesopotamia . El a provocat suparare in vechea sa patrie , prin invataturile sale si a fost exilat in sudul Italiei , unde a intemeiat scoala pitagoreicilor . Pitagoreicii cunosteau medicina egipteana veche .
“Hermes Trismegistos :
Este aceasta comprimarea si diluarea de care vorbea Thales ?
Nu se prezinta aici un principiu , necunoscut pina astazi de noi , al exploziei primordiale , al gaurilor negre si al contractiei sau expansiunii spatiului ?
Eudoxus din Cnidus ( 408 – 355 BC ) , a petrecut 16 luni in Egipt unde a studiat astronomia . A fost discipolul lui Archytas din Tarent .
Anaximandru ( 610-547 BC )
1
Egiptenii cunosteau valoarea lui π pentru care foloseau valoarea 3 ----
6
Un papyrus egiptean demonstreaza ca egiptenii puteau calcula valoarea ariei unui cerc , folosind
1
numarul transcendental π pentru care foloseau valoarea 3 -----
6
Iata ce continea acest vechi papirus egiptean din Teba , al scribului Ahmose din timpul celui de al 15 reprezentatant al dinastiei Hyskos , faraonul Apepi I . Ahmose a afirmat in papirusul sau ca scrierea lui este similara celei din timpul lui Amenemhet III ( 1842 – 1797 b.c. ) .
Papirusul matematic din Rhynd
Problema Calculations showing 2 divided by each of the odd numbers in turn from 3 to 100 Les calculs montrant 2 se sont divisés par chacun des nombres impairs à leur tour 3 100
- A table showing the results of dividing each of the numbers from 1 to 9 by 10 Une table donnant les résultats de diviser chacun des nombres de 1 à 9 par 10
- Show how some of (a) above were calculated: 1, 2, 6, 7, 8, 9 divided by 10 Montrez comment une partie (a) de ci-dessus a été calculée : 1, 2, 6, 7, 8, 9 s'est divisé par 10
1 - 6 Show the multiplication of various fractions by either 1 /2 /4 or 1 //3 /3 Montrez la multiplication de diverses fractions par 1/2 /4 ou 1 //3 /3
7 - 20 Problems of completion i.e. fraction subtraction Problèmes de soustraction de fraction d'accomplissement c.-à-d.
21 - 23 Quantity problems e.g. a quantity is added to a seventh of that quantity and the result is 19. Des problèmes de quantité par exemple une quantité est ajoutés à un septième de cette quantité et le résultat est 19.
30 - 34 Similar to 24 - 27 but involve more fractional parts of x Semblable à 24 - 27 mais impliquent des parties plus partielles de x
35 - 38 Hekat problems Problèmes de Hekat
39 Division of loaves
Division des pains
40 Division of loaves involving arithmetical progression Division des pains impliquant la progression arithmétique
41 - 43 Volume of cylindrical granaries Volume de greniers cylindrique
44 - 46 Volume of rectangular granaries Volume de greniers rectangulaires
47 Division of 100 hekat Division du hekat 100
48 Area of a circle and its circumscribing square Secteur d'un cercle et de sa place d'entourage
49 Area of a rectangle Secteur d'un rectangle
50 Area of a circle Secteur d'un cercle
51 Area of a triangle Secteur d'une triangle
52 Area of a truncated triangle Secteur d'une triangle tronquée
53 Area of sections of a triangle Secteur des sections d'une triangle
54 - 55 Division related to area Division liée au secteur
56 - 60 Pyramid problems Problèmes de pyramide
61 - 87 Miscellaneous problems Problèmes divers
Background
The papyrus was found in Thebes in the ruins of a small building near the Ramesseum. It is a copy made by the scribe Ahmose during the 15th Dynasty reign of the Hyksos Pharaoh, Apepi I. Ahmose states that his writings are similar to those of the time of Amenemhet III (1842 - 1797 b.c.).
The papyrus, written in hieratic the cursive form of hieroglyphics, is a single roll which was orginally about 5.4 metres long by 32 centimetres wide.
Contents
Note: The Ancient Egyptians used only unit fractions which are here represented by a stroke line followed by the denominator e.g. a thirteenth=/13. Two thirds was the only common exception to this rule and is here represented by two stroke lines preceding the number 3=//3 .
Below you will find that:
1 and a half and a quarter is represented by 1 /2 /4.
1 and two thirds and one third is repesented by 1 //3 /3.
Pina aici , deocamdata
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
Euclid (365 – 300 BC ) , fondatorul universitatii din Alexandria . Primul matematician care a demonstrat ca exista o infinitate de numere prime . In cartea sa Elements , Euclid arata de o maniera foarte ingenioasa ca exista o infinitate de numere prime : oricare ar fi un numar prim p , suita finita a numerelor prime pina la p ,
2 , 3 ,5, 7 ,11 , 13 ,17 , … , p ,
nu contine totalitatea numerelor prime .
Intradevar , inmultind intre ele toate aceste numere si adaugind 1 , obtinem un numar N care este fie numar prim fie este divizibil cu un numar prim , ca orice numar superor lui 1 .
N = 2 x 3 x 5 x 7 x 11 x 13 x 17 x … x p + 1 .
Dar , N nu este divizibil cu nici un numar prim din suita , prin constructie ( N mod p = 1 , p = 2, 3, 5, 7 ,… , p ) . Astfel , orice nou divisor al lui N , trebuie sa fie un numar pim . Intr-un cuvint , orice lista finita cu numere prime nu este completa .
Pithagora ( 580 – 500 BC ) a calatorit in Egipt , unde a ramas 22 de ani si a fost initiat ca Mare Preot
.
The Riemann Hypothesis is a true matematical statement .
************************************************************************************************************
The Riemann Hypothesis is a true matematical statement .
************************************************************************************************************
The Riemann hypothesis as it is , can not be proven .
The Riemann Hypothesis as it is :
The Riemann Hypothesis : If ρ € C \ {1} is a nontrivial zero of ζ(ρ) = 0 , then R(ρ) = 1/2 .
The Riemann hypothesis as it is , can not be proven .
************************************************************************************************************
The Riemann Hypothesis as it is :
The Riemann Hypothesis : If ρ € C \ {1} is a nontrivial zero of ζ(ρ) = 0 , then R(ρ) = 1/2 .
Andre Weil , unul din marii matematicieni ai secolului XX care , in anul 1940 , a demonstrat Ipoteza Riemann intr-un cadru geometric particular .
“ Quand j`etais jeune , j`esperais demontrer l`hypothese de Riemann . Quand je suis devenu un peu plus vieux , j`ai encore eu l`espoir de pouvoir lire et comprendre une demonstration de l`hypothese Riemann . Maintenant , je me contenterais bien d`apprendre qu`il en existe une demonstration . “
What is the connexion between mathematics and Starry Night painted by Van Gogh . Think about ! No clue ?
The eImage of Starry Night is comprresed using programs dedicated to this aim . These programs have been developed only after Fractals break through the world scene . Fractals enabled the techniques of commpresing images . See . It`s easy .
Van Gogh - Starry Night
This image is a photomosaic of the famous painting 'Starry Night'. The image is made with over 210.000 tiny photographs and a total size of over 1.500.000.000 points in other words it is a 1.5 Gigapixel Image. Click over the image (Zoom In) until you start to see the tiny images.
You`ll see about 20 images . Enjoy it . Enjoy the life . A unexpected conexion between mathematics and wonderful pets it will be revealed to you later . Till than smile and bright up the life of someone at whom you care by mailing eImages .
Life
In life there are moments, when you miss
someone so much, that you wish you could
grab them out of your dreams and hug them tight
When a door closes,
Another one opens,
But often we stand there so long looking
at the closed door,
That we do not see that one that’s opened.
Do not look at physical appearances,
they can be deceiving.
Do not look at riches,
For they are only temporary.
Look for someone who makes you smile.
Because sometimes it only takes a smile
to brighten up a very dark day.
Look for someone who makes
your heart sing.
Dream what you want to dream;
Go where you want to go;
Try to be who you really are; Because life is short, and often only gives one chance to do things..
I wish you in life a lot of luck to feel good;
Many trials to remain strong;
Some tears to remain human;
Lots of hope, to become happy.
The most splendid future will always depend
Upon the necessity to release the past;
You cannot move forward in life
Unless you learn from your past mistakes
and move on.
TrT T
T The The The really lucky people do not necessarily have the best of everything;
They are the ones who make the most of
whatever life throws at them.
The most splendid future will always depend
Upon the necessity to release the past;
You cannot move forward in life
Unless you learn from your past mistakes
and move on.
Send this message to people whom you really care about.
… as I have done …
… to those who have made an impact
on you in some way or another.
…to those who made you smile when you really needed it;
…to those who make you see the positive side of everything just when you’ve hit rock bottom. .
…to those whom you can’t do without.
And even if you don’t send it to anyone, do not
worry, nothing bad will happen.
You just waste the possibility of brightening up
someone’s life for a day!
Life is not measured with the quantity of breaths you take,
but with the quantity of moments that took your breath away!
Therefore…
Good Luck …
http://www.sharedivinelove.blogspot.com
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is the conexion ? You live on this planet about many years , isn`t that right . Along with cats and dogs . Did you really noticed them ?.
Voila : ( Ebosa ) Noua Theorema a celor 4 Culori
The New Theorem of the 4 Colours .
Numarul maxim de culori de pe blana mamiferelor terestre este de 4 ( combinatiile dintre 2 culori sunt doar amestecuri si nu le numaram ; fara nuante deci . Nuantele nu sunt culori in adevaratul sens al cuvintului )
The clue : Quantization .
There is a critical ratio
Number of bits necessary to write down in DNA a genetic characteristic
____________________________________________________________________________________________ ≤ h
Gains offered by this characteristic in the struggle of perpetuation of specie in the ecosystem
The value of h remain to be established .
Gains offered by this characteristic in the struggle of perpetuation of specie in the ecosystem .
The value of “ Gains” will be evaluated by giving marks .
Pisica mea Monica m-a facut sa ma gindesc la aceasta teorema !
Go out on the street and look at them . You will be amazed .
END OF STORY
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