calculateprimes    sub-page 

James M. McCanney, M.S. Physics

This web page was created to convey information to the public regarding a topic which affects your life every day of the year.  Since the dawn of Civilization, Prime Numbers have stood as one of the great unsolved mysteries of modern man.  The Ancient Greeks understood that there were infinitely many Prime Numbers, but did not know where they came from or why they refused to show any order.  Every great mathematician up to modern times has searched for a formula or concept that would unlock the enigma of the Prime Numbers.  They are used today as the "keys" of modern "encryption" codes that allow secure internet transactions and other forms of secure communications.  Modern supercomputers calculate larger and larger Prime Numbers, but give little understanding of the order of these strange and illusive numbers.

The book and DVD lecture presented in this web page are the public release of information already passed within very limited and controlled inner circles.  Patent, Trademark and Copyright work has preceded the release of this information to the general public (see Copyright - Patent - Trademark - Notice below).     

The standard mathematical definition of a prime number is basically any number that has only itself and 1 as factors.  Examples are 2, 3, 5, 7, 11, 13, 17, etc.  After many decades of research ... the mysteries of the prime numbers have finally been solved and are presented in the book with 3 hour lecture DVD entitled .."CALCULATE PRIMES".  

The implications of the solution method are far reaching, having applications in scientific fields as diverse as Quantum Mechanics and Genetics.  Everything in Nature is controlled by repeatable processes, although the outcomes may vary.  Will a diamond produced on the far side of the Universe have the same properties as a diamond found on earth.  Why are snowflakes and Galaxies similar?  There is far more contained in this book and DVD than just the solution to an age old mathematical problem.  It suggest the workings of Nature are far more subtle than you ever imagined. 


when this book DVD set was released i introduced it to my audience ... i invited my good friend and nationally known talk show host Brad Walton to conduct the interview ... listen to this two hour interview if you have time (link follows - 14 MByte file download 2 hour play time MP3 format) ----> CalculatePrimesBradWaltonInterviewMarch2007.mp3

*** to purchase the book find the order button below ***

NOTE - in March of 2014 i released the second book in this series titled "Breaking RSA Codes for Fun and Profit" which describes in detail how to break RSA encryption codes and also takes you into the dark nefarious world of computer security ... available in eBook format on the sales page (only available on this web page)

OTHER RELEASES TO FOLLOW


"Calculate Primes" BOOK and DVD combination - Details and Order Sub Page

This book has been written for the general public.  The "Calculate Primes" book is 93 pages of text including a 10 page preface that relates parts of my past not made public before ... there are 20 chapters and the DVD includes a lecture approximately 3 hour long plus my January 11, 2007 radio show on the topic of "repeatability" ... a topic that is central to the release of the new book ... the original mathematical treatise is included as an appendix for more technically oriented readers ... this is far more than a solution to the oldest mathematical problem ... it also gives direction to fundamental properties of nature that are seen in every aspect of science ... jim mccanney

The front and rear book covers and table of contents as well as the Introduction and Preface by the Author are listed below.  At the very bottom of this page is a list of prime numbers up to 9109.

*** ORDER BUTTON IS AT THE BOTTOM OF THIS PAGE ***

 



                               TABLE OF CONTENTS

I.              THE ANCIENT GREEKS AND THE PRIMES

II.             ABOUT THE INCLUDED DVD LECTURE

III.            THE PRIME NUMBER TABLE

IV.            COPYRIGHTS PATENTS AND TRADE MARKS

V.              DISCOVERY OF THE MAGIC NUMBERS

VI.            0 AND 1  THE BUILDING BLOCKS

VII.           THE GENERATOR FUNCTION

VIII.          PROPERTIES OF PRIME NUMBERS

IX.             FACTORIZATION & THEOREM OF PRIMES

X.              SNOWFLAKES - SYMMETRY and PRIMES

XI.            THE RIEMANN HYPOTHESIS

XII.           QUANTUM MECHANICS AND GENETICS

XIII.          REPEATABILITY IN NATURE

XIV.          THE WAVE NATURE OF PRIME NUMBERS

XV.           OLD METHOD OF DETERMINING PRIMES

XVI.         THE FUTURE OF PRIMES

XVII.        ENCRYPTION - IS IT DOOMED?

XVIII.      APPENDIX I - THE ORIGINAL MATHEMATICAL TREATISE

XIX.         OTHER SOURCES OF INFORMATION

      XX           0 & 1 & NEGATIVE AND COMPLEX PRIMES                                                                                                                                                                                                                                                                                                                                                                                                                                                         

About the author and this text:

This book, as promised, will present to the public a rarely seen side of the author.  James McCanney is known worldwide for his research and books as well as radio and lecture appearances dealing with the electrical nature of the cosmos.  What many people do not know is that he is also a Mathematician who has worked on and solved some of the more complex problems of Physics and Mathematics, and is an expert in computer design, solid-state physics, telecommunications and computer protocols. 

He has worked about half of his lengthy career in private industry, owning several of his own companies and also taught at the University level in Physics, Mathematics, Computer Science and Astronomy.  Much of this was accomplished in multi-lingual settings, having worked in the USA, Latin America and with high-level Russian scientists.  He has presented his findings at numerous international conferences and is a regular presenter at American Geophysical Union meetings.  He has presented his theoretical research in locations such as Los Alamos National Laboratories, International Air shows and International Electric Propulsion conferences.  Understanding his background is important in placing the current text into perspective.

James M. McCanney, M.S. received sound classical physics training at St. Mary's University (Winona, Minnesota) receiving a Bachelor of Arts degree with a double major in Physics and Mathematics in 1970.  He was offered full scholarship awards to three major US physics graduate schools to pursue his graduate physics studies.  However, he chose instead to postpone graduate studies for a period of three years while he traveled and taught Physics and Mathematics in Latin America.

During this time he spent a good deal of  time traveling to ruins of ancient cities and archeological sites, studying firsthand many times as the ruins were dug from under dirt that had not been moved for thousands of years.  Also during this time he developed the basis for his theoretical work that would, at a later date, deal with the celestial mechanics of N-bodies and plasma physics, as well as the groundwork for the current treatise on prime numbers. 

He has stated that in his travels he learned that nature provides elegant yet simple solutions to even the most complex problems, and that she reveals these fundamental secrets to only those who pursue truth for truth�s sake, without the encumbrances of modern life or economic rewards that so many times cloud the visions of humans, especially scientists, most of whom are entrenched in the age of big business and government monopolized science.

With this new understanding of archeology, astronomy of the ancients, physics and the world around him, Mr. McCanney returned to graduate school in 1973 and earned a Master of Science degree in nuclear and solid-state physics from Tulane University, New Orleans, LA.  His research involved a National Institute of Health research grant (in conjunction with Gulf South Research Institute) to study visible light and x-ray sensitive photo polymers to be used in medical Xerox x-ray machines.  The results of his research resulted in patented discoveries. He was again offered a full fellowship to continue on with Ph.D. studies, but once again he declined and returned to Latin America to study archeology and teach Physics, Mathematics and Computer Science in Spanish.  He continued his personal work to explore the mysteries of celestial mechanics and its relationship to the planets, moons and other celestial bodies.

At this time a fellow Ph.D. at Tulane wrote in a letter to a professor at another University, the first observation that comes to mind concerning Jim McCanney is his unusually broad range of scientific and intellectual interests.  His mind is a veritable fund of information and ideas on topics as varied as Egyptian pyramids and the classification of mushrooms.  His character and morals are of the highest caliber.  He possesses an excellent aptitude for design and construction of research and measurement systems as well as a creative bent in understanding and explaining observed physical processes.  He is able to engage in significant research with little or no direct supervision.  His research experience is such that he could involve undergraduates with minimal outlay of funds.  He has the ability to command respect of those in his classes and is able to generate an unusually good rapport with students.

After four years living and teaching at the university level in Latin America, in 1979 Mr. McCanney joined the faculty of Cornell University, Ithaca N.Y. as an introductory instructor in physics.  It was during this time that he had access to NASA data returning daily from the Voyager I and II spacecraft as they traveled by the planets Jupiter, Saturn and beyond (as well as data from many other space craft).  It was here he recognized that the mathematical models in his theoretical work regarding the electro-dynamic nature of the solar system and universe had its signatures in the new data that was streaming in from the edges of the solar system.

His papers were published at first in the peer reviewed astrophysical journals, but soon he began to receive resistance from the standard astronomical community.  Mr. McCanney was removed from his teaching position because the standard scientific community did not accept his beliefs regarding the electro-dynamic nature of the solar system, beliefs that are just now becoming the basis for modern Space Science and Astrophysics. 

His innovative theories on plasma physics and a new model for fusion in the solar atmosphere provided the basis for the electric fields and plasma discharge phenomena that have become the core elements of his theoretical models of the true nature of the solar system in which we live, and which are the fast becoming the basis for every international conference on space weather and space physics. 

Upon being removed from the physics department for his then radical beliefs, Mr. McCanney was rehired shortly thereafter by the mathematics department also at Cornell University, where he taught for another year and a half and continued to publish his papers in peer reviewed astrophysical journals.  Again astronomers coerced his removal from the Mathematics Department and ultimately he was blackballed from publishing in the astrophysics journals in1981. 

His first peer-reviewed paper in 1980 "Continuing Galactic Evolution" (written while he was in the Physics Department but published while in the Mathematics Department of Cornell University) advanced a new technique for solving simultaneous differential equations for the orbits of stars in a galaxy.  It is said that only a small handful of people in the world understood the significance of this short but important paper.  With a second paper "Saturn's Sweeper Moons Predicted", he was, according the department chairman at the time, the only Cornell Mathematics Department faculty member ever to be published in the peer reviewed astrophysics journals.

During this time Mr. McCanney established himself as the originator of the theoretical work regarding the electrical nature of the cosmos for which he coined the term "THE ELECTRIC UNIVERSE", which today is being proven correct on an ongoing basis by space-probes returning data from outer space.  Many of his predictions such as x-rays to the sunward side of comet nuclei, that comet nuclei would be found to have no ice or water frozen on their surfaces and that comets interact electrically with the Sun as well as solar electrical activity affecting Earth weather, have now been confirmed by direct measurements in 1986, 1996, 2001 and 2002 to the present day.  Many other more abstract concepts have also been verified.

After the Cornell years Mr. McCanney worked in the telecommunications industry as a Principle Systems Engineer at a major telecommunications corporation designing computer telecommunications equipment, and also ran a number of his own companies dealing with satellite communications and electrical propulsion systems.  He attended and spoke at numerous international conferences on the future of space flight using his designs of electro-magnetic propulsion. 

It was during these same years that he continued to interact with the scientists at Los Alamos Labs and Goddard Space Flight Center during the era of the first comet fly bys of comets Giacobini-Zinner and Comet Halley.  Throughout the years and the decades, he has always remained an Independent Scientist, never using government funding or positions to further his personal research.

In the mid-1990s Mr. McCanney's work was recognized by a group of high-level Russian scientists at the University at Novosibirsk who had measured but did not understand electro-dynamic effects around Earth and in the solar system.  Upon discovering Mr. McCanney's work, they translated all of his papers to date into Russian. These are still being taught at the university level as the leading edge of research in this field.  It is only due to the ongoing and intentional efforts of NASA that his work has received such little attention in the western scientific community and press.

In the background Mr. McCanney continued working on the illusive mathematical problems facing celestial mechanics, that is, the unknown method of solving simultaneous differential equations.  He believed that nature had provided a simple but elegant method to solve these complex problems that did not exist in current mathematical capabilities.  He envisioned a mathematical technique that would be applied and reapplied to generate a final solution.  In this respect, many unsolved problems of mathematics and quantum mechanics and even genetic molecular structures would have their solutions in this new mathematical technique. 

His search lead to a technique that is the basis for the discovery of the solution to the prime number problem presented in this book, and which now holds promise at solving some of the great mysteries of Quantum Physics as well as Genetics.  It is based on the Mathematical Operators that the Professor calls "Generator Functions". 

These mathematical expressions operate on fundamental units or building blocks of nature such as the numbers 0 and 1 (as in the case of the prime number solution in this book) or atomic nuclei (in the case of quantum mechanics) or atoms and small molecules (in the construction of large organic molecules or genetic structures).  According to Mr. McCanney, the Generator Function is an operator that reflects conditions in nature, it builds up a first layer when applied to the basic building blocks, and then is applied to this construct to form a second more complex structure.  The same Generator Function is then reapplied to this result and the process continues, with each successive application modifying the prior set of results. 

This leads to questions that are being asked for the first time.  For example in genetics, could the makeup of the human biped be not only duplicated somewhere else in the universe, but is the norm rather than the exception based on "Generator Functions" that operate on the building blocks of life.  Could this pattern be replicated on the far side of the universe just as a diamond would appear the same in such a distant place?

On a simpler note, as the prime numbers would be discovered by intelligent beings on the far side of the universe, they would follow the same mathematical Generator Function that we would discover here on earth.  The implications of this new mathematical technique may someday very well overshadow this initial application and the discovery of the formula for directly calculating the prime numbers to infinity as presented in this book and DVD lecture (Appendix I contains the original mathematical treatise).

An essential aspect of the Generator Function concept is that it creates intermediate or false solutions that are necessary steps to generate the final correct solution.  This is possibly but one of the reasons why so many mathematicians have worked around the prime number problem without finding a solution, as they failed to see the total picture as presented in this book.  Countless mathematicians have come to the conclusion that that prime numbers are random with but passing patterns.  This book proves that to be incorrect.  When you finally look at the prime number table and see why every number is there and how it is related to all the other primes, with all of their "ancestors" bridging back to the numbers 0 and 1, you will understand the powerful impact this book will have on the future.

This is a brief but incomplete history of the background that makes The Professor, as many people call Mr. McCanney, a person with a unique background and qualifications.

Mr. McCanney airs a weekly radio show "The James McCanney Science Hour - At the Crossroads" heard world wide on short wave radio and also broadcast on the internet.  He has been a popular regular guest on many national and international radio shows.  Most people know of "The Professor" from his work regarding the electrical nature of outer space and its relation to our planet and human beings that inhabit our blue planet. 

He has worked over his career on the current topic of the prime number solution and has taught the following mathematics courses at the University level (in addition to Physics, Computer Science and Astronomy); Abstract Algebra, Linear Algebra, Matrix Algebra, Probability and Statistics, Statistics for Computing, Mathematical Logic, Theory of Numbers, Calculus I, II and III, Engineering Math I and II, Advanced Topics in Geometry and Topology.

He has been an avid student of the history of both Physics and Mathematics and has studied the past to understand what is of greatest importance in the future of these fields of study.  The present book is a glimpse into this rarely seen side of Professor McCanney.  He has stated that his greatest discoveries to date include the cause of surface fusion on the sun, which gives rise to the solar electric field that drives the electrical nature of the solar system.  His second great discovery, which was published almost 2 decades before its discovery, was the prediction that comets would produce x-rays far to the sunward side, as well as the electrical nature of comets and the prediction that comet nuclei would not contain water or ice, but would be hot dry asteroid type bodies (a prediction that has repeatedly been proven by subsequent space probes), much to the surprise of professional astronomers. 

A third major theoretical discovery, which has been observed both in nature and subsequently measured in the laboratory, he calls "The Induced Electric Dipole Red Shift".  This is an effect on photons of light moving through a non-uniform electric field that causes both a red shift as well as a bending of light.  It also explains the previously unknown cause of pair production (electron-positron production) in photons passing near heavy atomic nuclei.  His theoretical work then restructures the laws of cosmology based on this new form of red shift.  

And last but not least, his work has rediscovered the work of Tesla and further provides a theoretical basis for deriving unlimited electrical energy from the ionosphere.  Another result of his decades of research has been the realization that severe earth weather including hurricanes and tornados are powered by electrical discharges from the ionosphere to the clouds in storm systems.  The list of scientific discoveries also includes an electromagnetic propulsion system for use in space travel that has been field-tested.

In spite of these discoveries that were confirmed in many cases decades after Mr. McCanney's theoretical predictions were published, he now has stated that the current treatise on prime numbers potentially may have the greatest significance in the history of both Physics and Mathematics.  The solution of the Prime Number Problem has eluded every great mind since the Greeks first defined it nearly 2500 years ago. Cauchy, Gauss, Riemann, Euler, and countless others spent their entire lives scouring this problem, yet could not crack the fundamental problem of being able to directly calculate the prime numbers.  Countless major unsolved problems in both Physics and Mathematics base their solutions on the prime numbers, yet no one could directly calculate these illusive and perplexing numbers, that is, until now. 

It was in quest of this solution and the understanding of its importance that has brought us to herald this work, which is now explained in a way that only the good Professor can do, making it understandable by anyone with a rudimentary knowledge of mathematics.  The solution is simple and elegant, the way nature intended.

At present there are two more books destined to become part of this series that will be released at later dates.

                                                                              a.s.


PREFACE

Putting this book into perspective

Preface by the Author

The solution to the prime number problem haunted me from my earliest introduction to it in late grade school or early high school. I had worked on trying to find patterns and certainly found myself "discovering" many of the same facets of the prime numbers and following many of the same false leads that the hundreds of mathematicians had stumbled upon over the past 2500 years.

In pursuit of a solution over many decades, I read everything that existed and got to know the paths of great mathematicians such as Gauss, Euler and Riemann, the same great names that brought us so many unbelievably complex advancements in every field of mathematics. Certainly the solution to understanding the primes had its base in the foundations put down by these greatest of mathematicians. My efforts of course came and went as I worked on other pursuits. I had to leave my prime number file on the shelf to collect dust only to return time and time again to take up the battle.

Then finally a number of years ago I sat and stared into a mental mirror and had to come to task with a fundamental issue. If all of these great mathematicians could not solve this problem, were they all wandering perhaps down the wrong roads? What were they all missing? I decided at that point on two issues, both of which later proved to be correct. The first was something I had discovered while wandering in the rain forests of Central America and camping in the remotest wilderness areas of northern Canada. This was the realization that the solution to understanding the prime numbers was like everything else in nature ... it most certainly did exist ... and it had to be elegant but simple. And secondly, there had to be a new "method" of mathematics that had not yet been discovered.

As I later found out, I was correct on both counts. So it was at that fateful point in my theoretical life that I made a conceptual decision that was the equivalent of cutting off my right arm. I would take indefinite leave of working on the project labeled "Prime Number Problem"  until such time as I had forgotten all of what had to be false leads of all these other mathematicians I had studied and likewise abandoned my own set of false leads.

Many times I had to resist the temptation to reopen the "Prime Number Problem" file as I saw it sitting on the shelf, since I had not shed myself of all the dead weight yet. Patience my son, patience a little voice said inside of my head. And I then continued with the many other pursuits that have kept me more than busy over the years.

Then one day, after possibly 2 years of not thinking about the prime number problem, I sat down with pen and paper and the solution starting flowing like water over a newly opened reservoir. I was setting on a deck in the warm sun, and with a fresh supply of paper, began putting together the pieces of the puzzle. In retrospect, at times I thought that there was one or another aspect of the total solution that was paramount or more important than any other, but in the final analysis there are so many subtle and intricate solutions that have to be woven together to make the final solution work, that it is not possible to weight any one aspect above the others. As with many events, it was a collection of factors all working in harmony to give the true vision of the prime numbers.

Little did I know that my brains had been purged of "the past prime number problem" information and the fresh look was truly what was needed. As I sat down that morning with pen in hand, I began probing into the middle of the prime number table. It hit me like a ton of bricks and I did not stop working until the entire solution method had been worked out ... it was so logical and so simple ... and so elegant.  I had solved the initial portion ... the essence of the prime number problem. It took another 6 weeks of daily work to iron out the details and put it into a form that other people would understand. Additionally I had to answer for myself all of the difficult questions I knew that professional mathematicians would ask when they saw the formula that directly calculates the prime numbers. Most of all, I had discovered a new mathematical technique that I knew had to exist and may possibly be used on other more complex mathematical problems.

This book has been designed for the general public and also for mathematicians who want an overview of the solution to the oldest and most illusive mathematical problem in the history of modern man.

jim mccanney



               List of Prime Numbers to 9109

     (print this list onto full size paper to perform exercises)



      2      3      5      7     11     13     17     19     23     29 



     31     37     41     43     47     53     59     61     67     71 



     73     79     83     89     97    101    103    107    109    113 



    127    131    137    139    149    151    157    163    167    173 



    179    181    191    193    197    199    211    223    227    229 



    233    239    241    251    257    263    269    271    277    281 



    283    293    307    311    313    317    331    337    347    349 



    353    359    367    373    379    383    389    397    401    409 



    419    421    431    433    439    443    449    457    461    463 



    467    479    487    491    499    503    509    521    523    541 



    547    557    563    569    571    577    587    593    599    601 



    607    613    617    619    631    641    643    647    653    659 



    661    673    677    683    691    701    709    719    727    733 



    739    743    751    757    761    769    773    787    797    809 



    811    821    823    827    829    839    853    857    859    863 



    877    881    883    887    907    911    919    929    937    941 



    947    953    967    971    977    983    991    997   1009   1013 



   1019   1021   1031   1033   1039   1049   1051   1061   1063   1069 



   1087   1091   1093   1097   1103   1109   1117   1123   1129   1151 



   1153   1163   1171   1181   1187   1193   1201   1213   1217   1223 



   1229   1231   1237   1249   1259   1277   1279   1283   1289   1291 



   1297   1301   1303   1307   1319   1321   1327   1361   1367   1373 



   1381   1399   1409   1423   1427   1429   1433   1439   1447   1451 



   1453   1459   1471   1481   1483   1487   1489   1493   1499   1511 



   1523   1531   1543   1549   1553   1559   1567   1571   1579   1583 



   1597   1601   1607   1609   1613   1619   1621   1627   1637   1657 



   1663   1667   1669   1693   1697   1699   1709   1721   1723   1733 



   1741   1747   1753   1759   1777   1783   1787   1789   1801   1811 



   1823   1831   1847   1861   1867   1871   1873   1877   1879   1889 



   1901   1907   1913   1931   1933   1949   1951   1973   1979   1987 



   1993   1997   1999   2003   2011   2017   2027   2029   2039   2053 



   2063   2069   2081   2083   2087   2089   2099   2111   2113   2129 



   2131   2137   2141   2143   2153   2161   2179   2203   2207   2213 



   2221   2237   2239   2243   2251   2267   2269   2273   2281   2287 



   2293   2297   2309   2311   2333   2339   2341   2347   2351   2357 



   2371   2377   2381   2383   2389   2393   2399   2411   2417   2423 



   2437   2441   2447   2459   2467   2473   2477   2503   2521   2531 



   2539   2543   2549   2551   2557   2579   2591   2593   2609   2617 



   2621   2633   2647   2657   2659   2663   2671   2677   2683   2687 



   2689   2693   2699   2707   2711   2713   2719   2729   2731   2741 



   2749   2753   2767   2777   2789   2791   2797   2801   2803   2819 



   2833   2837   2843   2851   2857   2861   2879   2887   2897   2903 



   2909   2917   2927   2939   2953   2957   2963   2969   2971   2999 



   3001   3011   3019   3023   3037   3041   3049   3061   3067   3079 



   3083   3089   3109   3119   3121   3137   3163   3167   3169   3181 



   3187   3191   3203   3209   3217   3221   3229   3251   3253   3257 



   3259   3271   3299   3301   3307   3313   3319   3323   3329   3331 



   3343   3347   3359   3361   3371   3373   3389   3391   3407   3413 



   3433   3449   3457   3461   3463   3467   3469   3491   3499   3511 



   3517   3527   3529   3533   3539   3541   3547   3557   3559   3571 



   3581   3583   3593   3607   3613   3617   3623   3631   3637   3643 



   3659   3671   3673   3677   3691   3697   3701   3709   3719   3727 



   3733   3739   3761   3767   3769   3779   3793   3797   3803   3821 



   3823   3833   3847   3851   3853   3863   3877   3881   3889   3907 



   3911   3917   3919   3923   3929   3931   3943   3947   3967   3989 



   4001   4003   4007   4013   4019   4021   4027   4049   4051   4057 



   4073   4079   4091   4093   4099   4111   4127   4129   4133   4139 



   4153   4157   4159   4177   4201   4211   4217   4219   4229   4231 



   4241   4243   4253   4259   4261   4271   4273   4283   4289   4297 



   4327   4337   4339   4349   4357   4363   4373   4391   4397   4409 



   4421   4423   4441   4447   4451   4457   4463   4481   4483   4493 



   4507   4513   4517   4519   4523   4547   4549   4561   4567   4583 



   4591   4597   4603   4621   4637   4639   4643   4649   4651   4657 



   4663   4673   4679   4691   4703   4721   4723   4729   4733   4751 



   4759   4783   4787   4789   4793   4799   4801   4813   4817   4831 



   4861   4871   4877   4889   4903   4909   4919   4931   4933   4937 



   4943   4951   4957   4967   4969   4973   4987   4993   4999   5003 



   5009   5011   5021   5023   5039   5051   5059   5077   5081   5087 



   5099   5101   5107   5113   5119   5147   5153   5167   5171   5179 



   5189   5197   5209   5227   5231   5233   5237   5261   5273   5279 



   5281   5297   5303   5309   5323   5333   5347   5351   5381   5387 



   5393   5399   5407   5413   5417   5419   5431   5437   5441   5443 



   5449   5471   5477   5479   5483   5501   5503   5507   5519   5521 



   5527   5531   5557   5563   5569   5573   5581   5591   5623   5639 



   5641   5647   5651   5653   5657   5659   5669   5683   5689   5693 



   5701   5711   5717   5737   5741   5743   5749   5779   5783   5791 



   5801   5807   5813   5821   5827   5839   5843   5849   5851   5857 



   5861   5867   5869   5879   5881   5897   5903   5923   5927   5939 



   5953   5981   5987   6007   6011   6029   6037   6043   6047   6053 



   6067   6073   6079   6089   6091   6101   6113   6121   6131   6133 



   6143   6151   6163   6173   6197   6199   6203   6211   6217   6221 



   6229   6247   6257   6263   6269   6271   6277   6287   6299   6301 



   6311   6317   6323   6329   6337   6343   6353   6359   6361   6367 



   6373   6379   6389   6397   6421   6427   6449   6451   6469   6473 



   6481   6491   6521   6529   6547   6551   6553   6563   6569   6571 



   6577   6581   6599   6607   6619   6637   6653   6659   6661   6673 



   6679   6689   6691   6701   6703   6709   6719   6733   6737   6761 



   6763   6779   6781   6791   6793   6803   6823   6827   6829   6833 



   6841   6857   6863   6869   6871   6883   6899   6907   6911   6917 



   6947   6949   6959   6961   6967   6971   6977   6983   6991   6997 



   7001   7013   7019   7027   7039   7043   7057   7069   7079   7103 



   7109   7121   7127   7129   7151   7159   7177   7187   7193   7207 



   7211   7213   7219   7229   7237   7243   7247   7253   7283   7297 



   7307   7309   7321   7331   7333   7349   7351   7369   7393   7411 



   7417   7433   7451   7457   7459   7477   7481   7487   7489   7499 



   7507   7517   7523   7529   7537   7541   7547   7549   7559   7561 



   7573   7577   7583   7589   7591   7603   7607   7621   7639   7643 



   7649   7669   7673   7681   7687   7691   7699   7703   7717   7723 



   7727   7741   7753   7757   7759   7789   7793   7817   7823   7829 



   7841   7853   7867   7873   7877   7879   7883   7901   7907   7919 



   7927   7933   7937   7949   7951   7963   7993   8009   8011   8017 



   8039   8053   8059   8069   8081   8087   8089   8093   8101   8111 



   8117   8123   8147   8161   8167   8171   8179   8191   8209   8219 



   8221   8231   8233   8237   8243   8263   8269   8273   8287   8291 



   8293   8297   8311   8317   8329   8353   8363   8369   8377   8387 



   8389   8419   8423   8429   8431   8443   8447   8461   8467   8501 



   8513   8521   8527   8537   8539   8543   8563   8573   8581   8597 



   8599   8609   8623   8627   8629   8641   8647   8663   8669   8677 



   8681   8689   8693   8699   8707   8713   8719   8731   8737   8741 



   8747   8753   8761   8779   8783   8803   8807   8819   8821   8831 

       8837        8839         8849        8861        8863        8867        8887         8893        8923         8929

       8933          8941         8951       8963         8969        8971        8999         9001        9007        9011

       9013          9029         9041        9043         9049       9059        9067         9091        9103         9109


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