Lucas-Lehmer numbers

[AntonioLao]

In the search for prime numbers among all Mersenne numbers to which can be primes or composites, an effective test for primality is known as the Lucas-Lehmer test. For an integer N the Lucas-Lehmer number is given by L(N)=L(N-1)-2. That is the square of the previous Lucas-Lehmer number minus 2, for examples, L(3)=14 where the previous LL-number is L(2)=4, 4=16 and 16-2=14 and it is divisible by the Mersenne prime 2-1=7, L(4)=194 where the previous LL-number is 14, L(5)=37634 where the previous LL-number is 194, and L(6)=1416317954 where the previous LL-number is 37634. Among these four LL-numbers, it can be demonstrated by simple calculations that even LL-numbers failed the test while the odd ones passed. Although this cannot be used to test all the consecutive primes, on the other hand, it can assert that all Mersenne numbers passing the test can be used to find all their associated perfect numbers. They are numbers that are equal to the sum of their positive divisors but not including the number itself, for examples: 6=1+2+3, 28=1+2+4+7+14, and 496=1+2+4+8+16+31+62+124+248. It can be noted that among these perfect numbers at the least two of their addends are primes. The largest prime to date that passes the Lucas-Lehmer test was discovered in the internet at http://www.mersenne.org/ see also the following links:
http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
http://mathworld.wolfram.com/Lucas-LehmerTest.html
http://primes.utm.edu/largest.html

[mkirkpatrick]

What's in a number? All or nothing,prehaps all numbers
are relatively real only,in absolute terms number or numbers
are non-existant,how could any mere number even reflect
that which just IS!



regards michael.

[AntonioLao]

What's in a number?

In the prehistoric era, numbers were used for counting the number of sunrises and sunsets before the new moon or the full moon as ways of keeping track of the ocean tides and seasons while other creatures seem to response to natural changes without the use of numbers. Even the cicadas have life cycles of prime numbers 13 and 17 years. http://en.wikipedia.org/wiki/Cicada and http://en.wikipedia.org/wiki/Circadian_rhythm

[Graybeard]

Strangely enough ... The Australian Aboriginals, known to have been here for 40K years, with new evidence pointing to 60K ... never invented/developed a system of maths.

And yet they must have counted, but how ???

cool bananas ... greg

[AntonioLao]

And yet they must have counted

Numbers seem to be responsible for the rise and fall of organized civilizations. The falls of the Roman Empire might be attributed to their number system: I, II, III, IV, V, VI, VII, VIII. IX, X, D, L, C, and M. This system can't go beyond 99 thousands.

[Pankter]

x = 2ʳ ̷ 4

If ( (2+√3)˟ + (2+√3)ˉ˟ ) / (2ʳ - 1) = I then (2ʳ - 1) = Prime

[Pankter]

(2+√3)˟ = a+ b√3 --> (a + b√3) + (a + b√3)ˉ¹ = i(2ʳ - 1) = z

a² + 2ab√3 + 3b² + 1 = z(a + b√3) -----> a² + 3b² - za + 1 = zb√3 - 2ab√3

√3 = (a² + 3b² - za + 1) / (zb - 2ab) ----> zb - 2ab = 0 --> z = 2a

b = √(a²-1) / √3

(2+√3)˟ = a + √(a²-1)


if 2a/(2ʳ - 1) = i then (2ʳ - 1) = p

[G_burnett]

can you explain please the r value etal power use? ty ... using a formula of any sort should maybe include the "Where ___ is " after to explain a bit more for clarity to me.
kind regards and welcome to the TOE Pankter .. g

[Pankter]

[Pankter]