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Whitebeard and Ace's past are shown: Ace was the captain of the Spade Pirates. Ace confronts Jimbei to meet Whitebeard since Ace turned down an offer to become a Warlord. Soon after Whitebeard offered Ace to join his crew when his battle has ended, Ace attempted to kill Whitebeard to no avail. Whitebeard allowed Ace to become a division commander.
Initial concept art for the Straw Hat Pirates. Several characters have been stated to be based on actual pirates and sailors such as: Eustass Kid (Eustace the Monk and William Kidd), X. Drake (Sir Francis Drake), Basil Hawkins (Basil Ringrose and John Hawkins), Capone Bege (Al Capone and William Le Sauvage), Jewelry Bonney (), Urouge (Aruj and Oruç Reis), Alvida (), Bartolomeo (Bartholomew ...
Whilst the book was being prepared for Bologna Book Fair, someone at Walker Books suggested the idea of adding a distinctive-looking character whom the reader could search for in the crowd scenes. [3] After much thinking, Handford came up with the idea of "Wally", a world traveller and time travel aficionado who always dresses in red and white. [4]
A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , ... ( OEIS : A038134 )
6×5 6546983 + 1 13 June 2020 4,576,146 63 4788920×3 9577840 – 1 14 February 2024 4,569,798 64 69×2 14977631 – 1 3 December 2021 4,508,719 65 192971×2 14773498 – 1 7 March 2021 4,447,272 66 4×3 9214845 + 1 10 September 2024 4,396,600 67 9145334×3 9145334 + 1 25 December 2023 4,363,441 68 4×5 6181673 – 1 15 July 2022 4,320,805 69
For example, the AP-3 with primes {3, 5, 7} and common difference 2# = 2, or the AP-5 with primes {5, 11, 17, 23, 29} and common difference 4# = 6. It is conjectured that such examples exist for all primes k. As of 2018, the largest prime for which this is confirmed is k = 19, for this AP-19 found by Wojciech Iżykowski in 2013:
In 1973, Denis Hanson proved that there exists a prime between 3n and 4n. [5] In 2006, apparently unaware of Hanson's result, M. El Bachraoui proposed a proof that there exists a prime between 2n and 3n. [6] El Bachraoui's proof is an extension of Erdős's arguments for the primes between n and 2n.
q-3, q-4, q-9, q-12 are quadratic nonresidues q-3, q-4, q-9, and, for q > 11, q-12 are primitive roots; If p is a Sophie Germain prime greater than 3, then p must be congruent to 2 mod 3. For, if not, it would be congruent to 1 mod 3 and 2p + 1 would be congruent to 3 mod 3, impossible for a prime number. [16]