**James M. McCanney, M.S. Physics**

The mathematical solution that I created to directly calculate prime numbers is 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”. Fundamental to the solution is a new definition of prime numbers since the old one is missing major components of these mysterious numbers. With the new view, the age old unsolved problems of prime numbers are now within reach.

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 in March of 2007 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 (included in the Education Program product with other lectures on prime numbers).

***** to purchase the book see the product purchase sub page**

**NOTE –**Subsequently, 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**

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.

***** 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.

### 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 9,109**

**List of Prime Numbers to 9,109**

**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
181 191 193 197 199 211 (continued below)
the point is to look at this list (as have 10s of thousands of mathematicians before you)
because once you see the solution unveiled these numbers will start to take order showing
mathematical properties in Groups, symmetry, reciprocity, closure, completeness and will
exibit a wave like nature similar to that found in Quantum Mechanics and a symmetry as
found in genetics and DNA, snowflakes and Galactic structures.
**

**233 239 241 251 257 263 269 271 277 281 179 181 191 193 197 199 211 223 227 229 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 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 153 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
9013 9029 9041 9043 9049 9059 9067 9091 9103 9109**

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