Rigidity matroid

Prime gap function

In number theory, Firoozbakht’s conjecture, also known as the Firoozbakht conjecture, states that $p_n^{1/n}$ (where $p_n$ is the nth prime) is a strictly decreasing function of n, i.e.,

$p_n^{1/n}>p_{n+1}^{1/(n+1)}$ for all $n\ge 1.$

Equivalently: $p_{n+1}<p_n^{1+1/n}$ for all $n\ge 1.$

Another equivalent statement, ${\left(\frac{p_{n+1}}{p_n}\right)}^n<p_n$ for all $n\ge 1,$ is the motivating reason for the sequence Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland..

The conjecture is named after Farideh Firoozbakht, from the University of Isfahan, who stated it in 1982. If this conjecture is true, then the prime gap function $g_n=p_{(n+1)}-p_n$ satisfies $g_n<(\log p_n{)}^2-\log p_n$ which is sharper than Cramér's conjecture $g_n=O((\log p_n{)}^2).$ Currently, the largest stated verification was done by using "Maximal gaps between consecutive primes less than 4.444 * 10¹²" by Firoozbakht. Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended to all primes below 4Template:E.

The conjecture is believed to be false, as it contradicts the Cramér–Granville heuristic. If it were true it would imply the weaker Cramér conjecture.

See also

• Prime number theorem
• Andrica's conjecture
• Legendre's conjecture
• Oppermann's conjecture

Notes

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References

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43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.