Mersenne primes have a close connection to perfect numbers, which are numbers equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if "M" is a Mersenne prime then "M"("M"+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist (If it exist, it would have to be greater than 10).
It is currently unknown if there is an infinite number of Mersenne primes. Most mathematicians who have studied the question think there are an infinite number of Mersenne primes. Carl Pomerance, Samuel S. Wagstaff Jr. and Hendrik Lenstra developed a formula which they think should say about how many Mersenne primes there are under a given number.
The binary representation of 2 - 1 is "n" repetitions of the digit 1.
For example, 2 - 1 = 11111 in binary.
The first four Mersenne primes were known by the Ancient Greeks. They are 3, 7, 31 and 127. The next, 8191, was discovered in 1456. Some people like trying to find big primes. Since there are tricks and algorithms to finding Mersenne primes quickly, the largest known primes are also Mersenne primes.
As of December 21, 2018, 51 Mersenne primes have been found. The largest known prime is a Mersenne prime, formula_1.
Insolation
Insolation is derived from the words "incoming solar radiation". Insolation is specifically applied to radiation which is arriving at earth’s atmosphere first and then earth's surface. The heat is derived from solar energy, normally called solar radiation. Insolation is the solar radiation that reaches the earth's surface. It is measured by the amount of solar energy received per square centimetre per minute. Similarly, solar energy received by the earth is called insolation. It is the amount of incoming solar radiation that is received over a unit area of the earth’s surface. Solar energy received over the planet’s surface varies according to season, latitude, transparency of the atmosphere, and aspect or ground slope.
Insolation affects temperature. The more the insolation, the higher the temperature.
In any given day, the strongest insolation is received at noon.
The amount of insolation received on the earth’s surface is not uniform everywhere. It varies according to the place and time. When the tropical regions receive maximum annual insolation, it gradually decreases towards the poles. Insolation happens more in summers and less in winters. The major factors which influence the amount of insolation received are:
At the top of the earth’s atmosphere received insolation is expressed as the solar constant. It receives at the top of the atmospheric surface (thermopause) on a perpendicular plane to the solar beam. The average insolation received at the thermopause i.e.1368Wm2(Watt per squaremetre)energy(solar constant) is in the form of short wave. Thus, it is termed as solar constant for that mean distance from the sun. These solar constant is varying over 1 Wm2 by periodic disturbances and explosions in the solar surface basically related to sun spot. Sun spots are dark and cooler areas visible on the sun’s surface.The recent researches have shown that more and more energy is released when the sunpots are in large number.The number of sunspots also increases or decreases on a regular basis, creating a cycle of 11 years.
Since the earth is a geoid resembling a sphere, the sun’s rays strike the surface at different angles at different places. This depends on the latitude of the place.The higher the latitude, the less is the angle they make with the surface of the earth.
The area covered by the vertical rays is always less than the slant rays. If more area is covered, the energy gets distributed and the net energy received per unit area decreases. Moreover, the sun’s rays with small angle traverse more of the atmosphere than rays striking at a large angle.
The length of the day determines the duration of sunlight which affects the amount of solar radiation received by the earth’s surface. The longer period of sunshine, greater the quantity of solar radiation will be received by a portion of earth.For example, at the equator the length of days and nights is 12 hours in all the months but the tropics of Arctic and Antarctic sunshine duration varies between 0 and 24. On the autumn and springe quinoxes (September 23and March 21 respectively),the sun is overhead at the equatorat noon.The night and day all over the earth are equal on these days and maximum amount of insolation is received at the equator, and the amount of insolation decreasing towards the poles.It is caused by vertical sunshine at equator but with increasing latitudes, the rays become more and more slanting. Therefore, poleward, the received energy keeps on declining.
The earth is revolving around the sun in an elliptical orbit, resulting continuous change in the distance between sun and the earth on annual basis. It leads to seasonal variation in solar energy received by the earth.The mean distance between the earth and sun is about 149,600,000 kilometers(92,900,000 miles).When earth position is farthest(152 million km) from sun is known as ‘aphelion’ on July 4. It is perihelion(147 million km)occurs on January 3 each year which is the closest distance. During aphelion the northern hemisphere is facing the sun and therefore receives energy about 7 percent less than the perihelion (southern hemisphere).
Atmosphere is not transparent for all the radiation coming from the sun because of different composition and layers. It is also one of the controlling factors of insolation to reach earth surface. The atmosphere is composed of gases, water vapour and particulate matters.The atmosphere is a mixture of gases,such as nitrogen(N), oxygen (O2), Argon, carbon dioxide, Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr), Ozone (O3), Nitrous oxide (N2O), Hydrogen (H) and Xenon (Xe). The atmosphere also contains water vapour, water in the gaseous state.
The longer the duration of daylight, the more the insolation received per day.
The Settlers II
The Settlers II is a real-time strategy (RTS) computer video game. It was released by Blue Byte Software in 1996.
Hugo Chávez
Hugo Rafael Chávez Frías (IPA: ) (July 28, 1954 – March 5, 2013) was president of Venezuela from 1999 until his death in 2013. He was the leader of the "Bolivarian Revolution" and promoted his vision of democratic socialism, Latin American integration, and anti-imperialism. Chávez was also an ardent critic of neoliberal globalization and U.S. foreign policy.
Chávez was a career military officer. He founded the left-wing Fifth Republic Movement after a failed coup d'état against former President Carlos Andrés Pérez. Chávez was elected to serve as president in 1998. This was mainly because he promised to help the poor majority of Venezuelan people. He was re-elected in 2000, and 2006.
He started a movement called Bolivarian Missions. Its goal is to fight disease, illiteracy, malnutrition, poverty, and other social problems. Abroad, Chávez is known for supporting alternative models of economic development. He also spoke in favor of a collaboration of poor nations, especially those in Latin America. On September 20, 2006, Chávez made a speech to the UN General Assembly. Chávez said that U.S. President George W. Bush is "The devil came here yesterday, and it smells of sulfur still today".
Chávez's reforms have caused controversy, both inside Venezuela, and outside the country. Some people criticized the reforms, others supported them. Those people who support the reforms say that he has given more power to the poor, and that he has stimulated economic growth. Those who argue against the reforms say that he is an autocrat who has mismanaged the economy.