Prime Arithmetic Progression
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
…shades of night.
“The sky grew darker, painted blue on blue, Continue reading
Waves – Lesson 1 – The Nature of a Wave
From Physics Classroom
Categories of Waves
Waves come in many shapes and forms. While all waves share some basic characteristic properties and behaviors, some waves can be distinguished from others based on some observable (and some non-observable) characteristics. It is common to categorize waves based on these distinguishing characteristics.
Longitudinal versus Transverse Waves versus Surface Waves
One way to categorize waves is on the basis of the direction of movement of the individual particles of the medium relative to the direction that the waves travel. Categorizing waves on this basis leads to three notable categories: transverse waves, longitudinal waves, and surface waves. Continue reading
Does Military Sonar Kill Marine Wildlife?
From Scientific American, June 10, 2009
Dear EarthTalk: Is it true that military sonar exercises actually kill marine wildlife? — John Slocum, Newport, RI
Unfortunately for many whales, dolphins and other marine life, the use of underwater sonar (short for sound navigation and ranging) can lead to injury and even death. Sonar systems—first developed by the U.S. Navy to detect enemy submarines—generate slow-rolling sound waves topping out at around 235 decibels; the world’s loudest rock bands top out at only 130. These sound waves can travel for hundreds of miles under water, and can retain an intensity of 140 decibels as far as 300 miles from their source.
These rolling walls of noise are no doubt too much for some marine wildlife. While little is known about any direct physiological effects of sonar waves on marine species, evidence shows that whales will swim hundreds of miles, rapidly change their depth (sometime leading to bleeding from the eyes and ears), and even beach themselves to get away from the sounds of sonar. Continue reading
How does sonar work?
From Science Wire
Sonar is simply making use of an echo. When an animal or machine makes a noise, it sends sound waves into the environment around it. Those waves bounce off nearby objects, and some of them reflect back to the object that made the noise. It’s those reflected sound waves that you hear when your voice echoes back to you from a canyon. Whales and specialized machines can use reflected waves to locate distant objects and sense their shape and movement.
The range of low-frequency sonar is remarkable. Dolphins and whales can tell the difference between objects as small as a BB pellet from 50 feet (15 meters) away, and they use sonar much more than sight to find their food, families, and direction. Continue reading
Reef on the brink
The Great Barrier Reef: a catastrophe laid bare
By Michael Slezak, 7 June 2016
Australia’s natural wonder is in mortal danger. Bleaching caused by climate change has killed almost a quarter of its coral this year and many scientists believe it could be too late for the rest. Using exclusive photographs and new data, a Guardian special report investigates how the reef has been devastated – and what can be done to save it
It was the smell that really got to diver Richard Vevers. The smell of death on the reef. “I can’t even tell you how bad I smelt after the dive – the smell of millions of rotting animals.” Continue reading
Who Was the Teacher of Righteousness in the Dead Sea Scrolls?
By Kerry A. Shirts, 1992 [Excerpted]
The Dead Sea Scrolls are documents (thousands of fragments) found in caves in the deserts of Palestine around Jerusalem, during the 1940’s-50’s, written by Jewish sectaries who fled to the wilderness in opposition to the prevailing powers at Jerusalem, and specifically the Temple, approximately 200 B.C. Samuel Sandmal, notes that it is clear the community of Qumran arose because of the dissatisfaction of how the priests were running the Temple. It had divine sanction, they did not.1
The scrolls contain instructions on how to live in order to be the receivers of a new covenant the sect felt was coming. In other words the documents seem to have an apocalyptic orientation. Every book of the Bible is represented except the Book of Esther, as well as many apocryphal books, commentaries on these books with their particular application to the sect (arguably the Essenes), sectarian materials on how to join the sect, etc. Continue reading
The Teacher of Righteousness
in the Qumran Texts
By F. F. BRUCE, 1957
I. THE TEACHER AND THE TEXTS
‘The Teacher of Righteousness’ is the name given in a number of the lately discovered Qumran documents to a man who was held in high veneration by the religious community on whose beliefs and practices these documents have thrown so much light. If he was not actually the founder of the community, it was certainly he who impressed upon it those features which distinguished it from other pious groups which flourished among the Jews during the last two or three centuries of the Second Commonwealth. So far as we can gather from our present sources of information, he is never referred to by his personal name in the Qumran texts.1
The title bestowed on him by his followers, ‘The Teacher of Righteousness’ (Heb. moreh sedeq or moreh hassedeq), may echo Hosea x. 12, where the prophet calls to his people: ‘break up your fallow ground: for it is time to seek the LORD, till he come and rain righteousness (Heb. yoreh sedeq) upon you.’ The RV margin gives ‘teach you righteousness’ as an alternative translation to ‘rain righteousness Continue reading
King James Bible
1. Habakkuk’s Complaint
1 The burden which Habakkuk the prophet did see. 2 O LORD, how long shall I cry, and thou wilt not hear! even cry out unto thee of violence, and thou wilt not save! 3 Why dost thou shew me iniquity, and cause me to behold grievance? for spoiling and violence are before me: and there are that raise up strife and contention. 4 Therefore the law is slacked, and judgment doth never go forth: for the wicked doth compass about the righteous; therefore wrong judgment proceedeth.
The Lord’s Answer
5 Behold ye among the heathen, and regard, and wonder marvellously: for I will work a work in your days, which ye will not believe, though it be told you. 6 For, lo, I raise up the Chaldeans, that bitter and hasty nation, which shall march through the breadth of the land, to possess the dwellingplaces that are not theirs. 7 They are terrible and dreadful: their judgment and their dignity shall proceed of themselves. 8 Their horses also are swifter than the leopards, and are more fierce than the evening wolves: and their horsemen shall spread themselves, and their horsemen shall come from far; they shall fly as the eagle that hasteth to eat. 9 They shall come all for violence: Continue reading