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Statements

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Firoozbakht's conjecture Гипотеза Фирузбэхт حدسية فيروزبخت Conjetura de Firoozbakht Conjecture de Firoozbakht Firoozbakhts förmodan
rdfs:comment
In number theory, Firoozbakht’s conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers. It is named after the Iranian mathematician Farideh Firoozbakht from the University of Isfahan who stated it first in 1982. The conjecture states that (where is the nth prime) is a strictly decreasing function of n, i.e., Equivalently: see OEIS: , OEIS: . If the conjecture were true, then the prime gap function would satisfy: Moreover: occurs infinitely often for any where denotes the Euler–Mascheroni constant. which is weaker, and which is stronger. في نظرية الأعداد، تنص حدسية فيروزبخت على أن (حيث هو العدد الأولي الذي يأتي في الرتبة n في لائحة الأعداد الأولية) هي دالة تناقصية قطعا. سميت هذه الحدسية هكذا نسبة إلى من جامعة أصفهان. حدسها عام 1982. En théorie des nombres, la conjecture de Firoozbakht est une conjecture relative à la distribution des nombres premiers, proposée en 1982 par la mathématicienne iranienne Farideh Firoozbakht, de l'université d'Ispahan. La conjecture énonce que la suite (où est le n-ième nombre premier) est strictement décroissante, soit encore : La conjecture implique que La conjecture de Firoozbakht est vérifiée pour tout Гипотеза Фирузбэхт — это гипотеза о распределении простых чисел. Гипотеза носит имя иранского математика Фариды Фирузбэхт (1962—2019) из университета в Исфахане, которая высказала её в 1982 году. Inom talteorin är Firoozbakhts förmodan en förmodan som säger att (där är det n:te primtalet) är en strikt avtagande funktion av n, det vill säga för alla Ekvivalenta former av förmodan är för alla och för alla Förmodandet är uppkallad efter som framlade det 1982. Om denna förmodan är sann satisfierar funktionen olikheten vilket är starkare än Cramérs förmodan
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In number theory, Firoozbakht’s conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers. It is named after the Iranian mathematician Farideh Firoozbakht from the University of Isfahan who stated it first in 1982. The conjecture states that (where is the nth prime) is a strictly decreasing function of n, i.e., Equivalently: see OEIS: , OEIS: . By using a table of maximal gaps, Farideh Firoozbakht verified her conjecture up to 4.444×1012. Now with more extensive tables of maximal gaps, the conjecture has been verified for all primes below 264 ≈ 1.84×1019. If the conjecture were true, then the prime gap function would satisfy: Moreover: see also OEIS: . This is among the strongest upper bounds conjectured for prime gaps, even somewhat stronger than the Cramér and Shanks conjectures. It implies a strong form of Cramér's conjecture and is hence inconsistent with the heuristics of Granville and Pintz and of Maier which suggest that occurs infinitely often for any where denotes the Euler–Mascheroni constant. Two related conjectures (see the comments of OEIS: ) are which is weaker, and which is stronger. Inom talteorin är Firoozbakhts förmodan en förmodan som säger att (där är det n:te primtalet) är en strikt avtagande funktion av n, det vill säga för alla Ekvivalenta former av förmodan är för alla och för alla Förmodandet är uppkallad efter som framlade det 1982. Om denna förmodan är sann satisfierar funktionen olikheten vilket är starkare än Cramérs förmodan En théorie des nombres, la conjecture de Firoozbakht est une conjecture relative à la distribution des nombres premiers, proposée en 1982 par la mathématicienne iranienne Farideh Firoozbakht, de l'université d'Ispahan. La conjecture énonce que la suite (où est le n-ième nombre premier) est strictement décroissante, soit encore : La conjecture implique que La conjecture de Firoozbakht est vérifiée pour tout Гипотеза Фирузбэхт — это гипотеза о распределении простых чисел. Гипотеза носит имя иранского математика Фариды Фирузбэхт (1962—2019) из университета в Исфахане, которая высказала её в 1982 году. في نظرية الأعداد، تنص حدسية فيروزبخت على أن (حيث هو العدد الأولي الذي يأتي في الرتبة n في لائحة الأعداد الأولية) هي دالة تناقصية قطعا. سميت هذه الحدسية هكذا نسبة إلى من جامعة أصفهان. حدسها عام 1982.
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