There was a story that ran on CNN.com the other day about Riemann's Hypothesis and how the Clay Mathematics Institute is offering $1 million for anyone who can prove it. A summary as to what this is about can be found at the Prime Pages by Chris K. Caldwell (University of Tennessee).
Since it's been a while since I did any Mystical Math, I thought it would be fun to add something here. Alas, and Alac, some things are just not for me to figure out. But there is a story that I believe is all about Prime Numbers disguised as Mose's (pbuh) encounter with his honey that could prove useful to someone with insight into the problem.
28 Qasas (Stories)
وَلَمَّا وَرَدَ مَاء مَدْيَنَ وَجَدَ عَلَيْهِ أُمَّةً مِّنَ النَّاسِ يَسْقُونَ وَوَجَدَ مِن دُونِهِمُ امْرَأتَيْنِ
تَذُودَانِ قَالَ مَا خَطْبُكُمَا قَالَتَا لَا نَسْقِي حَتَّى يُصْدِرَ الرِّعَاء وَأَبُونَا شَيْخٌ كَبِيرٌ 28:23
28:23 And when he (Moses) arrived at the Waters/Wells (مَاء also matter) of Madyan (مَدْيَنَ a location that happens to sound like median) he found there ( وَجَدَ there was/present) a portion ( أُمَّةً some; Nation) of the populace ( النَّاسِ people) Watering ( يَسْقُونَ ) and there was from among them ( مِن دُونِهِمُ not including them) 2 Women avoiding ( تَذُودَانِ keeping away/defending) it. He said, 'Why are you not Watering?{ مَا خَطْبُكُمَا not systemic (part of the system)/universal /complete; literally خَطْ بُكُمَا == line of you; مَا خَطْ بُكُمَا no line of yours}? She said, 'We do not water (our flock) until the herdsman ( الرِّعَاء shepherds) issue (forth) { يُصْدِرَ they leave; recede/number}, and our Father ( وَأَبُونَا our father/basis/foundation) is an Important Sheik ( شَيْخٌ كَبِيرٌ Primary Person; Big Chief/Very Old Man)."
Now, it seems that each time Moses has an encounter the characters he engages are very colorful (like his traveling companion earlier). Take this 'girl' he meets--why on earth would she mention that her Dad is like the Top Dog as an addendum to the basic question as to why she and her sister are not watering their flock (or bring up her father at all)? It doesn't follow logically in the course of a natural conversation, it reads and sounds a little forced even. Unless we take into consideration all the connotations of the word 'Prime', then it all makes sense: the watering, the chief, the number 2,... the Madyan (Median)!
Here is a brief run down of the word Prime and its meanings in Arabic: (those in red appear in some form in the story)
noun:
قمة
من الدرجة الأولى
من النوع الممتاز
جيد
عدد أولي +++prime numberفي صحة جيدة
verb:شغل مضخة +++'prime a pump'
أدار محرك مضخة +++'prime a pump/managed engine pump'
أعد للإ طلا ق+++'prepared for painting/lacquer'
أثار جدلا+++++'caused a sensation' lit. 'raised it very' the part جد appears in the word 'present'
مهد لإمر++++++means 'the cradle to the order of ' the part لإمر appears in the word '2 women'
سقى+++++'watering' this root appears in the words waters/wells/watering/ in Sign 28:23
عوم+++++'float/launch/prime'
طلع+++++meanings include: 'rise, ascend, prime, brief, go up, inform, be updated, be acquainted with...'
adjective:أولي
رئيسي ++++main, chief, prime, leading, foremost, fundamental, prefix-key; synonymous with the '2 Women's Father' in the story.
جوهري
أصم
أصلي
ممتاز
It does seem convoluted, but here is one take on it:
There is a population (set) of numbers; some are prime but 2 is not included when taking the median. The reason given is that 2 is not part of the system or in the line because it can only water (be part of the primes) when all of the other primes (the flock herds watering) have left/receded or been numbered i.e., accounted for; furthermore, it would appear that 2 has as its basis/foundation/precedent the most important prime or is in some way related to the biggest prime; or something someone who likes this sort of thing can tell me over a latte some day.
And WHAT does all this have to do with Area 51? Sign 28:23 just so happens to add up to...
The short answer is: The number 2 is in fact the greatest (largest) prime number. The number 1 is subprime and all the other prime numbers larger than 2 are post-primes (hyper-prime?) --
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Proof:
This can be proved from the definition basis as follows:
From the definition of prime (wolframalpha):
A prime number (or prime integer, often simply called a "prime" for short) is a positive integer
that has no positive integer divisor other than 1 and p itself.
Based on this first statement that would mean the number 2.
(More concisely, a prime number
is a positive integer having exactly one positive divisor other than 1) --
Based on this second statement that would mean the number 2.
For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization
), making 24 not a prime number.
Based on this third statement that would mean the number 2 is still the greatest prime number.
Since, realistically, and based on the example given, 13 does have a positive divisor other than itself and 1 and that is the number 2 (again).
Yet, unlike composite numbers, the number 24 is given in the example, 13 divided by 2 does yield a remainder. But factorization of such a number as 13 and other so-called 'primes' is similar to factorization of composite numbers with remainders.
In the example 24 factors to (2^3)*3 whereas numbers such as 13 factorization gives a pattern similar to (2^3) + (2^2) + 1 . (The greatest prime number 2 is the base for the factorization, bolstering its place as the greatest prime number since everything else can be expressed in terms of 2 (even 1, since 2^0=1).
The fact remains that any prime number larger than 2 is still divisible by an integer, that being 2, other than itself, but yields a remainder (akin to the Mod functions) which can be expressed in terms of 2, the greatest prime number.
_______________
The closest analogy (See The Lady of the Lake) to this thought is that should a circle become open at a point along its perimeter, the 2 end points of the perimeter can never match back up to the exact same place and point when rejoined to make the circle that it had been prior to becoming disconnected or severed--this also gives rise/credence as to why pi is such a fascinating irrational number.
It is the impetus as to why the decimal portion of pi is unpredictable and goes on forever.
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