Chris Peterson wrote:
"Leonhard Euler proved 2,147,483,647 to be prime."
I'm pretty sure this is how anybody would look after engaging in such a mathematical exercise.
He looks bald! Maybe he didn't like his head getting cold.
"Mad" is the word I'd use. And I don't mean angry.
"Maps" is the word I'd use.
"Three years after suffering a near-fatal fever in 1735, [Euler] became almost blind in his right eye,
but Euler rather blamed the painstaking work on cartography
he performed for the St. Petersburg Academy for his condition."
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<<On September 7 1783 Euler spent the first half of the day as usual.
He gave a mathematics lesson to one of his grandchildren, did some
calculations with chalk on two boards on the motion of BALLOONS;
then discussed with Lexell & Fuss the recently discovered planet URANUS.
About five o'clock in the afternoon he suffered a brain haemorrhage
and uttered only "I am dying" before he lost consciousness.
Euler died about eleven o'clock in the evening.>>
In the eulogy written for the French Academy by the French
mathematician and philosopher Marquis de Condorcet, he commented,
"il cessa de calculer et de vivre—..." : he ceased to calculate and to live.
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<<The first two Uranian moons, discovered in 1787, did not receive names until 1852, a year after two more moons had been discovered. The responsibility for naming was taken by John Herschel, son of the discoverer of Uranus. Herschel, instead of assigning names from Greek mythology, named the moons after magical spirits in English literature: the fairies Oberon and Titania from William Shakespeare's A Midsummer Night's Dream, and the sylphs Ariel and Umbriel from Alexander Pope's The Rape of the Lock (Ariel is also a sprite in Shakespeare's The Tempest). The reasoning was presumably that Uranus, as god of the sky and air, would be attended by spirits of the air. Subsequent names, rather than continuing the airy spirits theme (only Puck and Mab continued the trend), have focused on Herschel's source material. In 1949, the fifth moon, Miranda, was named by its discoverer Gerard Kuiper after a thoroughly mortal character in Shakespeare's The Tempest. The current IAU practice is to name moons after characters from Shakespeare's plays and The Rape of the Lock (although at present only Ariel, Umbriel, and Belinda have names drawn from the latter; all the rest are from Shakespeare). At first, the outermost moons were all named after characters from one play, The Tempest; but with Margaret being named from Much Ado About Nothing that trend has ended.>>
<<Leonhard Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. Euler is considered to be the pre-eminent mathematician of the 18th century and one of the greatest mathematicians ever. Euler worked in almost all areas of mathematics: geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes. Euler's name is associated with a large number of topics.
Euler is the only mathematician to have two numbers named after him: the immensely important Euler's Number in calculus, e, approximately equal to 2.71828, and the Euler-Mascheroni Constant γ (gamma) sometimes referred to as just "Euler's constant", approximately equal to 0.57721. It is not known whether γ is rational or irrational. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
Euler's eyesight worsened throughout his mathematical career. Three years after suffering a near-fatal fever in 1735, he became almost blind in his right eye, but Euler rather blamed the painstaking work on cartography he performed for the St. Petersburg Academy for his condition. Euler's vision in that eye worsened throughout his stay in Germany, to the extent that Frederick referred to him as "Cyclops". Euler later developed a cataract in his left eye, rendering him almost totally blind a few weeks after its discovery in 1766. However, his condition appeared to have little effect on his productivity, as he compensated for it with his mental calculation skills and exquisite memory. For example, Euler could repeat the Aeneid of Virgil from beginning to end without hesitation, and for every page in the edition he could indicate which line was the first and which the last. With the aid of his scribes, Euler's productivity on many areas of study actually increased. He produced on average, one mathematical paper every week in the year 1775 (at age 68 ).>>
Thank you neufer. I never realised there was such a history to (2^31)-1, despite Euler being one of my favourites. I recall first "discovering" its prime-ness as I was teaching myself how to program computers (a while ago now) and writing my own little prime number calculator.
Euler's story may also resonate with owlice for the saying "In regione caecorum rex est luscus" in her signature. But she is free to like whichever prime number she chooses and I shall resolve to stop playing match maker.
A nice prime just popped up in the board stats: Total posts 133213 Pretty, hmm? Happens to be the 12433rd prime, and 12433 is (you know I wouldn't mention this otherwise) also prime.
owlice wrote:
A nice prime just popped up in the board stats: Total posts 133213 Pretty, hmm? Happens to be the 12433rd prime, and 12433 is (you know I wouldn't mention this otherwise) also prime.
It's not as fun as 132233, however. Why is that?
Did you mean to say that 133213 is not as much fun as 132241
Ah, neufer, that's a nice one, too! 132241 is almost as much fun; I do like the number very much, but 132233 has a certain extra something about it that appeals to my inner child.
owlice wrote:
Ah, neufer, that's a nice one, too! 132241 is almost as much fun; I do like the number very much, but 132233 has a certain extra something about it that appeals to my inner child.
http://oeis.org/A108571 wrote:
Sequence: A108571: Any digit d in the sequence says: "I am part of an integer in which you'll find d digits "d".
One of my favorite sequences are numbers that describe previous numbers
1
(one one)11
(two ones)21
(One two, one one)1211
(one one, one two, two ones)111221
1, 11, 21, 1211, 111221, 312211, 13112221,...
Is there a number that describes itself?
Beyond wrote:
Even though "0" isn't a number, it seems to describe itself pretty well.
That's debatable:
"The word zero came via French zéro from Venetian zero, which (together with cypher) came via Italian zefiro from Arabic صفر, ṣafira = "it was empty", ṣifr = "zero", "nothing". This was a translation of the Sanskrit word shoonya (śūnya), meaning "empty". The first known English use was in 1598."
<<There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition having first appeared in the 19th century.
The use of a 0 digit in place-value notation (within other numbers) dates back as early as 700 BC by the Babylonians, but they omitted such a digit when it would have been the last symbol in the number. The Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628. However, 0 had been used as a number in the medieval computus (the calculation of the date of Easter), beginning with Dionysius Exiguus in 525, without being denoted by a numeral (standard Roman numerals do not have a symbol for 0); instead nulla or nullae, genitive of nullus, the Latin word for "none", was employed to denote a 0 value.
The first systematic study of numbers as abstractions (that is, as abstract entities) is usually credited to the Greek philosophers Pythagoras and Archimedes. Many Greek mathematicians did not consider 1 to be "a number", so to them 2 was the smallest number.
Several set-theoretical definitions of natural numbers were developed in the 19th century. With these definitions it was convenient to include 0 (corresponding to the empty set) as a natural number. Including 0 is now the common convention among set theorists, logicians, and computer scientists. Many other mathematicians also include 0, although some have kept the older tradition and take 1 to be the first natural number. The term counting number is also used to refer to the natural numbers (either including or excluding 0). Likewise, some authors use the term whole number to mean a natural number including 0; some use it to mean a natural number excluding 0; while others use it in a way that includes both 0 and the negative integers, as an equivalent of the term integer.>>
Last edited by neufer on Wed Nov 13, 2013 7:47 pm, edited 1 time in total.
Beyond wrote:
So what is a "0" in binary, a spacer :?:
It can acts as either a spacer or number in any base system.
It's always a number. "Spacer" isn't a very reasonable description of its use in place-value notation. A zero in the basen position reflects that there is a count- zero- of basen values making up the number.
Chris
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Chris L Peterson
Cloudbait Observatory https://www.cloudbait.com
Another way to look at this is to think of a byte (8 bits) of computer memory. Each bit can be set with a low (0) or high (1) voltage across it (typically ~5 volts is considered high, as I recall). So zero, in this context is really (binary) 00000000, with every bit in the byte set with a low voltage. If we set all the bits high, we get (binary) 11111111, or in decimal, [2^8]-1 = 255. And of course, there are (decimal) 254 other combinations of bit voltages, in between 0 and (decimal) 255.
Hmm... I wonder just how many bytes bites there are in a pizza. I would imagine more than the licks of an owl trying to get to the center of a tootsie roll pop. According to the commercial, it took the owl 3-licks, then and it was all over
).>>
and it was all over 
