Hi, there!
In retrospect, my matriculation number used to be always odd; quite often,
“23,” if I remember correctly. My family name “Yoshida” came almost the
last when put in alphabetical order starting with boys.
It would be accidental, which I am still ambivalent about now and can’t be
reasoned. Maybe it’s because an odd number is “Warikirenai” in Japanese,
or indivisible.
Today, let me challenge a word problem related to prime numbers. Read
my blog thoroughly until you’re convinced.
How many primes \(x\) are there for which \((x^{3} + 3)\) is prime?
Here is my solution to the problem.
When \(x = 2\), \(x^{3} + 3 = 11\).
When \(x = 3\), \(x^{3} + 3 = 30\).
When \(x = 5\), \(x^{3} + 3 = 128\).
When \(x = 7\), \(x^{3} + 3 = 346\).
Whichever prime numbers except \(2\) are put in \(x\), \(x^{3}\) becomes an odd
number, and “the odd number \((x^{3}) + 3\)” becomes an even number;
never an odd one.
Thus, there is only one prime number at \(x = 2\) for which \((x^{3} + 3)\) is
prime.
My prime consideration is to make my blog informative and instrumen-
tal. Let me bear in mind that a journey of a thousand miles begins with
a single step.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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