Category Archives: Language
Ancient Afrrican Medu Neter
English Vocab Builder
Ancestors=jer-tee-oo, Mother=Moot, Daughter=Saht, Sister=Senet, Wife=Hemet, Father=Yi-tef, Son=Sah, Brother=Sen, Husband=Hee.
1=wa, 2=sen, 3=shomt, 4=fe-doo, 5=dee-oo, 6=see-soo, 7=se-fek, 8=sheme, 9=pe-sej, 10=mej.
Re (Ray) or Aten=Sun, Moon=Iah (pronounced yah, sometimes ee-ah), Neter=God, Neteret=Goddess.
Bad=bin, good=ne fer, light=she-sep, dark=keke. Never=en sep. Yes=tee-oo, no=nen, help=sem, old=yah, new=mah-oot, Alter=sah-oot. Temple=er-per, library= per me-jat, house=per, lady=nebet, Land=ta, lord=neb, midwife=tee-jem set, Nysut=leader or royal one, Sky=pet, doctor=sewnu, house of life=per ankh. Continue reading
The hieroglyphic sign for “mountain” depicted to peaks with a valley running between them. This image approximated the hills that rose up on either side of the Nile valley.
Although the djew hieroglyph did portray the mountain ranges the Egyptians saw in their everyday lives, it also was a visualization of their cosmic beliefs. Symbolically, the “mountain” was an image of the universal mountain whose two peaks were imagined to hold up the sky. The eastern peak was called Bakhu, to the west was Manu. The ends of this great mountain were guarded by two lions who were called Aker. Aker was a protector of the the sun as it rose and set each day. Continue reading
Primes, Modular Arithmetic, and Public Key Cryptography
(April 15, 2004)
Every cipher we have worked with up to this point has been what is called a symmetric key cipher, in that the key with which you encipher a plaintext message is the same as the key with which you decipher a ciphertext message. As we have discussed from time to time, this leads to several problems. One of these is that, somehow, two people who want to use such a system must privately and secretly agree on a secret key. This is quite difficult if they are a long distance apart (it requires either a trusted courier or an expensive trip), and is wholly impractical if there is a whole network of people (for example, an army) who need to communicate. Even the sophisticated Enigma machine required secret keys. In fact, it was exactly the key distribution problem that led to the initial successful attacks on the Enigma machine.
However, in the late 1970’s, several people came up with a remarkable new way to solve the Continue reading
An arithmetic progression of primes is a set of primes of the form for fixed and and consecutive , i.e., . For example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression of primes with difference 210.
It had long been conjectured that there exist arbitrarily long sequences of primes in arithmetic progression (Guy 1994). As early as 1770, Lagrange and Waring investigated how large the common difference of an arithmetic progression of primes must be. In 1923, Hardy and Littlewood (1923) made a very general conjecture known as the k-tuple conjecture about the distribution of prime constellations, which includes the hypothesis that there exist infinitely long prime arithmetic progressions as a special case. Important additional theoretical progress was subsequently made by van der Corput (1939), who proved than there are infinitely many triples of primes in arithmetic progression, and Heath-Brown (1981), who proved that there are infinitely many four-term progressions consisting of three primes and a number that is either a prime or semiprime. Continue reading
Top 20 Arithmetic Progression of Primes
by Chris Caldwell
The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection’s home page. This page is about one of those forms.
Definitions and Notes
Are there infinitely many primes in most arithmetic progressions? Certainly not if the common difference has a prime factor in common with one of the terms (for example: 6, 9, 12, 15, …). In 1837, Dirichlet proved that in all other cases the answer was yes:
- Dirichlet’s Theorem on Primes in Arithmetic Progressions
- If a and b are relatively prime positive integers, then the arithmetic progression a, a+b, a+2b, a+3b, … contains infinitely many primes.