PPT-Number Theory T wo ancient problems

Factoring Given a number N express it as a product of its prime factors Primality Given a number N determine whether it is a prime Factoring is hard Despite centuries of efforts the fastest methods for factoring a number N take time exponential in number of bits of N. 5 15 million years ago brPage 4br ANCIENT FLORIDA 4 million years ago brPage 5br ANCIENT FLORIDA 4 25 million years ago brPage 6br ANCIENT FLORIDA 15 million years ago brPage 7br ANCIENT FLORIDA 150 100 thousand years ago brPage 8br PRESENT FLORIDA Dynasties, Philosophers . and Ancient Life. Geography. Huang He (Yellow River). Named for the rich yellow soil it carries . Runs from Mongolia to the Pacific Ocean. Chang Jiang (Yangtze River). . Runs east across Central China to the Yellow Sea. In ancient Egyptian times, gods were extremely important. in making the country run properly so the Egyptians . w. orshipped gods for just about everything- flooding, health, love, having babies, the sun, the sky and so on.. By Ashley Hales and Samantha Pass. Samuel . Taylor Coleridge: October 21, 1772 -July 25, . 1834. He studied at Jesus College where he met lifelong friend Robert . Southley. , who influenced a lot of his work. . Greece. Sparta was an ancient Greek polis that was . surrounded . by enemies, so Spartan citizens began preparing for war at birth. . Sparta Ancient . Greece. Spartan . rulers examined newborn babies to determine if they were healthy and . 6. th. Grade. Government. The government that we have in the United States was influenced by the democratic government that was formed in . Athens. around 500 B.C. . The . Greeks invented the idea of citizenship. They are the forefathers of many modern democracies.. TEMPLES. Ancient India – Achievements. Magnificent temples—both Hindu and Buddhist—were built all around India. They remain some of the most beautiful buildings in the world . today. Gupta. temples were topped by huge towers and were covered with carvings of the god worshipped inside. By Linda L. Tavares. Homes. Most homes in ancient Greece had a courtyard, which was the center of activity. Children could safely play outside in the warm climate. Homes were divided into areas for the men and areas for the women. The . Aging. Sociological Theories and Social Problems. Theory:. A statement about how and why specific facts are related.. A theory provides a framework for organizing facts, and in so doing, provides a way of interpreting reality.. AND. BY TAMARA. Ancient Egyptian Food. Vegetables . that were grown included; Radishes, coriander, cabbages, endive, watermelons, cucumbers, cabbage, beans and melons were very common and widely grown. Today, we know that magical dragons exist only in imagination and myth. They are . mythical. creatures. . But in ancient China, the people firmly believed that dragons were real and powerful. The dragon was the sign of the emperors. . Date Monday June 17 2013 till Thursday June 20 2013TimeVenue Included 2 Co31ee Breaks and a Lunch EE Short CourseTopics to be CoveredDue to the limited space RSVP is required byemailing the local coo in making the country run properly so the Egyptians . w. orshipped gods for just about everything- flooding, health, love, having babies, the sun, the sky and so on.. There were over 2000 gods- that’s a lot more than all of the gods in all of the different religions that exist nowadays! The gods were male, or female (goddesses) and were often shown as having the body of a human and the head of an animal or bird. . This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.
Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.
The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.
The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.
Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),
k and t are indices of prime numbers,
2n is a given even number,
k, t, n ∈ N.
If we construct ellipses and hyperbolas based on the above, we get the following:
1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.
2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.
Will there be any new thoughts, ideas about this?