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560. p. n. e. — Pizistrat zauzima Akropolu u Ateni i proglašava se tiranom. Zbačen je iste godine. 560. p. n. e. (procjena) — Izrađen je Moskofor sa Atenske ...
- Definition For Prime Numbers
- Definition For Natural Numbers
- Characteristics
- Applications and Properties
- Appearance
- See Also
- References
For the nth prime number pn, the primorial pn# is defined as the product of the first nprimes: 1. p n # = ∏ k = 1 n p k {\\displaystyle p_{n}\\#=\\prod _{k=1}^{n}p_{k}} , where pk is the kth prime number. For instance, p5#signifies the product of the first 5 primes: 1. p 5 # = 2 × 3 × 5 × 7 × 11 = 2310. {\\displaystyle p_{5}\\#=2\\times 3\\times 5\\times 7...
In general, for a positive integer n, its primorial, n#, is the product of the primes that are not greater than n; that is, 1. n # = ∏ p ≤ n p prime p = ∏ i = 1 π ( n ) p i = p π ( n ) # {\\displaystyle n\\#=\\prod _{p\\leq n \\atop p{\\text{ prime}}}p=\\prod _{i=1}^{\\pi (n)}p_{i}=p_{\\pi (n)}\\#} , where π(n) is the prime-counting function (sequence A00072...
Let p and q be two adjacent prime numbers. Given any n ∈ N {\\displaystyle n\\in \\mathbb {N} } , where p ≤ n < q {\\displaystyle p\\leq n
Primorials play a role in the search for prime numbers in additive arithmetic progressions. For instance, 2236133941 + 23# results in a prime, beginning a sequence of thirteen primes found by repeatedly adding 23#, and ending with 5136341251. 23# is also the common difference in arithmetic progressions of fifteen and sixteen primes. Every highly co...
The Riemann zeta function at positive integers greater than one can be expressed by using the primorial function and Jordan's totient function Jk(n): 1. ζ ( k ) = 2 k 2 k − 1 + ∑ r = 2 ∞ ( p r − 1 # ) k J k ( p r # ) , k = 2 , 3 , … {\\displaystyle \\zeta (k)={\\frac {2^{k}}{2^{k}-1}}+\\sum _{r=2}^{\\infty }{\\frac {(p_{r-1}\\#)^{k}}{J_{k}(p_{r}\\#)}},\\qua...
Dubner, Harvey (1987). "Factorial and primorial primes". J. Recr. Math. 19: 197–203.Spencer, Adam "Top 100" Number 59 part 4.Početna strana; Istaknuti članci; Portali; Kategorije; Nedavne izmjene; Nasumična stranica
10. milenij p. n. e. 10. milenij prije nove ere obuhvatao je godine od 10.000 pne do 9001. godine prije nove ere (oko 12 ka do oko 11 ka). Označava početak tranzicije iz paleolita u neolit kroz periode prijelaznog mezolita ( Sjeverna Evropa i Zapadna Evropa) i epipaleolita ( Levant i Bliski istok ), koji zajedno čine prvi dio epohe holocena ...
The Aetolian (or Aitolian) League ( Greek: Κοινὸν τῶν Αἰτωλῶν) [1] was a confederation of tribal communities and cities [2] in ancient Greece centered in Aetolia in Central Greece. It was probably established during the early Hellenistic era, in opposition to Macedon and the Achaean League. Two annual meetings were held at ...
586 p.n.e. - 573 p.n.e. – babilońskie oblężenie Tyru (miasto nie zostało zdobyte, lecz król Tyru - Itobaal III uznał władzę zwierzchnią Nabuchodonozora II) 560 p.n.e. – Lidyjczycy podbili Jonię; około 560 p.n.e. – wystąpienie Zaratusztry; 555 p.n.e. – wybuch powstania Persów przeciwko Medom
