Most of the fishing currently practiced in Japan is done by small vessels with a small number of fishermen (one or two). One of the most common fishing methods is longline fishing. However, this method requires the vessel to operate at a constant low speed because the depth of the hook must be kept constant while adjusting the speed of the fishing boat to the tidal current. In addition, because the vessel must maneuver and fish at the same time, automation is desired. Thus, we propose a robotic system that can control the depth of the trap at a constant depth even when the speed of the vessel and the current change, and that can successfully fish without the need for skilled fishermen. Fishing can be conducted regardless of the speed of the vessel, whereas currently it is controlled by the speed of the vessel and the tidal current. Therefore, it may contribute to proposing new fishing methods as well as the existing ones. This can contribute to the shortage of successors to the fishing industry and to the revitalization of the fishing industry.

In solving the Collatz conjecture, it turns out that if we let all integers k be 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5, then we can solve the Collatz conjecture periodically. The Collatz conjecture states that for any positive integer P (initial value), if n is even, divide n by 2; if n is odd, repeat the rule of multiplying n by 3 and adding 1, which always converges to 1. One open problem has been proved by this paper. The authors hope to contribute to the mathematical community by presenting simple proofs of conjectures in the history of mathematics such as the Collatz conjecture.

A prime number is a natural number with no divisors other than itself and the number 1. There are many unsolved problems related to prime numbers. One such problem is finding a general method for identifying prime numbers. Although it is known that all prime numbers fall under the categories of 2, 3, or 6n±1 (where n≥1), a formalized method for eliminating composite numbers (non-prime numbers) from these categories has yet to be developed. This paper aims to explore a possible method for such elimination, which involves checking whether there exists an n that satisfies n = 6km+k+m or n = 6km+k-m (where k and m are non-zero integers). This method is expected to be a major step forward in the derivation of prime numbers.