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દુનિયાની સૌથી મોટી અવિભાજ્ય સંખ્યા(Prime no.)

ગણિતના ખાંટુઓની રેસ અવિરત ચાલુ જ છે.

દુનિયાની સૌથી મોટી અવિભાજ્ય સંખ્યા શોધવાની

      જો કે, એ બધા ખાંટુઓને એ પણ ખબર છે કે, કોઈ સૌથી મોટી સંખ્યા, કદી શોધી શકવાનું જ નથી, સાવ સાદા કારણે કે, અનંત સંખ્યાઓની જેમ અવિભાજ્ય સંખ્યાઓ પણ અનંત જ છે ! આથી ‘શેર’ને માથે ‘સવાશેર’ મળી જ જવાનો છે.

    પણ  ૨૫, જાન્યુઆરી – ૨૦૧૩ના રોજ શોધાયેલી દુનિયાની સૌથી મોટી અવિભાજ્ય સંખ્યા આ રહી…

prime

 

આખી સંખ્યા અહીં લખી શકાય એમ નથી!

એનું કારણ જાણવા તમારે આદમ સ્પેન્સર, સિડની – કોમેડિયન/ ટીવી શો એનાઉન્સર / આંક્ડાના કીડાને સાંભળવા જ પડશે–

આદમ સ્પેન્સર

આદમ સ્પેન્સર

આ ખોપરી વિશે…

   Adam Spencer is the breakfast host on 702 ABC Sydney, the most listened-to talk show in Australia’s biggest and most competitive market — but (or maybe because) in between the usual fare of weather, traffic and local politics he weaves a spell of science, mathematics and general nerdery. Really! In a radio landscape dominated by shock jocks and morning zoos, he plays eclectic tunes, talks math, and never misses the chance to interview a Nobel Prize winner. Which is unsurprising once you find out that this former world debating champion had actually started on a PhD in Pure Mathematics before he began dabbling in improv comedy, which eventually led to his media career.

 

 

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2 responses to “દુનિયાની સૌથી મોટી અવિભાજ્ય સંખ્યા(Prime no.)

  1. pragnaju સપ્ટેમ્બર 4, 2013 પર 12:58 એ એમ (am)

    M૫૭૮૮૫૧૬૧ ૧૭,૪૨૫,૧૭૦
    ૨૫૭,૮૮૫,૧૬૧ કરતા મોટો હશે.
    It is known that no non-constant polynomial function P(n) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is as follows: Suppose such a polynomial existed. Then P(1) would evaluate to a prime p, so P(1) \equiv 0 \pmod p. But for any k, P(1+kp) \equiv 0 \pmod p also, so P(1+kp) cannot also be prime (as it would be divisible by p) unless it were p itself, but the only way P(1+kp) = P(1) for all k is if the polynomial function is constant.

    The same reasoning shows an even stronger result: no non-constant polynomial function P(n) exists that evaluates to a prime number for almost all integers n.

    Euler first noticed (in 1772) that the quadratic polynomial

    P(n) = n2 − n + 41

    is prime for all positive integers less than 41. The primes for n = 1, 2, 3… are 41, 43, 47, 53, 61, 71… The differences between the terms are 2, 4, 6, 8, 10… For n = 41, it produces a square number, 1681, which is equal to 41×41, the smallest composite number for this formula. If 41 divides n it divides P(n) too. The phenomenon is related to the Ulam spiral, which is also implicitly quadratic, and the class number; this polynomial is related to the Heegner number 163=4\cdot 41-1, and there are analogous polynomials for p=2, 3, 5, 11, \text{ and } 17, corresponding to other Heegner numbers.

    It is known, based on Dirichlet’s theorem on arithmetic progressions, that linear polynomial functions L(n) = an + b produce infinitely many primes as long as a and b are relatively prime (though no such function will assume prime values for all values of n). Moreover, the Green–Tao theorem says that for any k there exists a pair of a and b with the property that L(n) = an+b is prime for any n from 0 to k − 1. However, the best known result of such type is for k = 26:

    43142746595714191 + 5283234035979900n is prime for all n from 0 to 25 (Andersen 2010).

    It is not even known whether there exists a univariate polynomial of degree at least 2 that assumes an infinite number of values that are prime

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