Lucky Numbers in Mathematics
According to number theory, a lucky number refers to a natural number that exists in a set. This set is usually generated by a specific “sieve.” In terms of its meaning, this sieve is generally very similar to the Sieve of Eratosthenes. The Sieve of Eratosthenes is known for generating primes and for eliminating numbers based on their position in a set. Contrary to famous conjecture, this elimination is not done based on a number’s value or its position in the original set of natural numbers, but on the basis of their position, as mentioned earlier.
This term was initially introduced in 1956 through a paper written by Gardiner, Lazarus, Metropolis, and Ulam. These personalities suggested calling the term its defining sieve, “the sieve of Josephus Flavius.” This suggestion came in the wake of potential similarities of this phenomenon with the counting-out game in the Josephus problem.
Lucky numbers are known to share some of their properties with prime numbers. For instance, their asymptotic behavior is very similar to the conduct of prime numbers. This property has been postulated in the prime number theorem as well. In fact, a version of Goldbach’s attributes has also been extended to these numbers. There are an infinite number of lucky numbers in the universe. However, mathematically speaking, if Ln is supposed to denote the nth lucky number, and Pn represents the nth prime number, then Ln will always be greater than Pn. Although, this statement is only applicable under the condition that N is a sufficiently large number.
Considering the fact that these lucky numbers are very well related to prime numbers, some mathematicians have also suggested that their properties might also be present in a more extensive set of numbers. Sieves of a specific anonymous form generate these larger sets of numbers. Notably, even though there has been a lot of conjecture around these stipulations, the theoretical framework is as scarce as before. Twin lucky numbers and twin primes are other examples of numbers occurring in similar frequency.
Lucky Numbers in Numerology
According to the study of numerology, all the numbers associated with a positive vibe or a relatively good impact on an individual’s life are said to be lucky numbers. These numbers are highly dependent on the belief and the faith that an individual has in their potency. Most individuals are designated individual and specific lucky numbers based on their names, date of birth, or astrological signs.
Some of the most commonly referred lucky numbers in numerology are — 1, 3, 7, 9, 13, 15, 21, 25, 31, 49, 51, 63, 67, 69, 73, 75, 33, 37, 43, 79, 87, 93, 99, and so on.
Contextually, particular numbers are posited as lucky in specific instances, such as —
In the Eastern and Chinese cultures, the number eight is supposed to be a lucky one because its pronunciation is close to the word “wealth.”
Five is another popular number in the universe because of its multiple appearances in nature. For instance, human beings have five senses — sight, smell, taste, touch, and hearing; and five fingers on each of their hands. Some fascinating creatures like the starfish exist with five-fold symmetry. The five-fold symmetry means that one can rotate a starfish five times, and it will come back to its original position.
Another fascinating number is seven, which is also observed in one’s surroundings. For instance, the seven wonders of the ancient world and the seven different notes in a harmonic octave. Additionally, there are also the seven natural colors present in white light. Other examples include seven skies, seven days a week, and seven seas.
The number nine is another number associated with positive vibes and the potential for a promising future. In Chinese culture, this number is linked with good news because it sounds the same as the word “long-lasting.”
The number 666 is a fascinating number because of its dual nature in the world. While western cultures avoided the number 666, Asian cultures associate this number with prosperity. According to the Christian Bible, western cultures avoid this number because this number is the number of the beast and Satan. Asian cultures associate this number with peace, luck, and prosperity because its pronunciation is very close to the phrase “things going smoothly.”