Why is the number '4' so prominent in the Death Note?

Question

In Death Note (TV Series 2006–2007), there is a pattern in a lot of the numeric references in the rules of the Death Note, where they relate to the number 4 in some way:

If the cause of death is written within the next 40 seconds of writing the person's name, it will happen.

After writing the cause of death, details of the death should be written in the next 6 minutes and 40 seconds [= 400 seconds total].

If a human uses the note, a god of death usually appears in front of him/her within 39 days [under 40 days] after he/she uses the note.

The Death Note will be rendered useless if the victim's name is misspelled four times.

If you lose the Death Note or have it stolen, you will lose its ownership unless you retrieve it within 490 days [a year and 4 months].

If writing the same name on more than two Death Notes is completed within a .6 seconds [0.4 seconds away from 1], it is regarded as simultaneous; the Death Note will not take effect and the individual written will not die.

Those with the eye power of the god of death will have the eyesight of over 3.6 [0.4 away from 4] in the human measurement, regardless of their original eyesight.
_{—"Rules of the Death Note", Death Note Wiki}

There are a few instances where other significant numbers ("magical number" 3, and "devil number" 6) are used, but none are quite as prevalent as 4.

Is this prevalent pattern a coincidence, or is there some significance to the number 4 that would be relevant in Death Note?

Answer 1

Because apparently, Four is Death. from the TV Tropes page of the same name:

In most Chinese languages and languages that borrow words from it, the words for "four" (四) and "death" (死) are written differently but pronounced similarly (somewhat like "sì" in Mandarin, "sei" in Cantonese, "shi" in Sino-Japanese, "tư" in Sino-Vietnamese, and "sa" in Sino-Korean). As a cultural trope, East Asian works of media tend to treat the number in much the way Western writers treat the number 13 (a number that Arabian and European culture consider Magical, and usually in a bad way).

Answer 2

According to the Wikipedia page for Japanese superstitions, in Japanese culture, the number 4 is an unlucky number because it is sometimes pronounced shi, which means death.

Also, in the Wikipedia page for Tetraphobia (the fear of the number 4):

The Chinese word for four (四, pinyin: sì, jyutping: sei3), sounds quite similar to the word for death (死, pinyin: sǐ, jyutping: sei2), in many varieties of Chinese. Similarly, the Sino-Japanese, Sino-Korean, and Sino-Vietnamese words for four, shi (し, Japanese), and sa (사, Korean), sound similar or identical to death in each language (see Korean numerals, Japanese numerals, Vietnamese numerals).

Essentially, the number 4, thanks to how it can be pronounced, is associated with death in a lot of East-Asian countries, particularly Japan, which is where the manga, Death Note, and the anime in question are produced. As the name of the manga/anime implies, death is one of the main themes in the story. It is thematically appropriate that the numeric references made in the Death Note hold this cultural significance and association with death.