CalculatePrimesCoversandTableofContents

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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