Are you one of the hopefuls who bets of the Powerball jackpot that climbs ever month? You probably have a hard time deciding on the lucky numbers that you will choose for your lottery ticket.
According to a news from abc7news published on March 28, 2019, someone from Wisconsin has won the $768.4 million jackpot in the Powerball. The said jackpot prize is considered the third-largest US lottery prize in history. You might be overwhelmed, but this is just half of the amount of money that you might be lucky to have if you were the winner of the record US lottery in January 2016 that had awarded $1.59 billion. (click here for more details)
Is it really about the lucky numbers? Or someone is just destined to be the receiver of that huge amount of money?
There is a number theory were these lucky numbers came from. These numbers are in a set which is generated by a particular “sieve.” Sieve is like the Sieve of Eratosthenes that makes the primes but eliminates numbers based on their position and not their value in the remaining set.
Gardiner, Lazarus, Metropolis, and Ulam, introduced the term in a paper in 1956. They also suggested calling it “sieve” because of its similarity with the counting-out game “the sieve of Josephus Flavius” in the Josephus problem. (click here for more details)
There are some categories of numbers that are generally termed “lucky numbers.” Euler’s lucky numbers are the first, and the second is obtained by taking out 1, 3, 5, 7, 9, 11, 13, and all odd numbers. Three is the first odd number greater than 1, so take out every third number: 1, 3, 7, 9, 13, etc. So these numbers are called lucky numbers 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, etc.,(OEIS A000959). These numbers share many asymptomatic properties of the prime numbers.
The asymptotic density is 1/lnN, similar to the prime number theorem, the frequency of twin primes, and twin lucky numbers. A version of the Goldbach conjecture also holds this. Thus, appearing that the sieving process accounts for many properties of the primes. (click here for more details)
If there’s this concept of lucky numbers, then there are unlucky numbers. And you probably already thought of a number. It is number 13!
Don’t go to the 13th floor. It’s not safe to go out for a trip on a Friday the 13th. According to researchers, at least 10 percent of the US population fear the number 13. This phobia for number 13, called paraskevidekatriaphobia, results in financial losses over $800 million annually, as people avoid marrying, traveling, or in the most severe cases, even working. (click here for more details)
Is 13 a cursed number? When did this fear start?
Some scientists and mathematicians point to the preeminence of number 12, which considered a perfect number in the ancient world. The ancient Sumerians’ numeral system is based on the number 12 that is still used for measuring time today, such as in our calendar, 12 months of the year, 12 hours is to half a day, etc. (click here for more details)
Some argue that 13 is found to be lacking and unusual.
Here are some of the probable reasons why people fear the number 13.
In the time of Jesus, there were 13 guests in the Last Supper, and either Judas Iscariot, who betrayed Jesus, or Jesus himself who was crucified, was seated on the 13th chair during the last supper. Often in the Bible, the number was not a positive reference. Some believed that the Crucifixion and the Last Supper occurred on the 13th. Bible scholars date that they happened in the 13th of Nisan (a month in the Jewish calendar)
Historian Vincent Foster Hopper points out that 16th-century numerologist Petrus Bungus is a firm believer of 13 as an unlucky number. Bungus, according to Hopper, recorded that the Jews murmured 13 times against God in the Exodus, so the thirteenth psalm concerns wickedness and corruption, which the circumcision of Israel occurred in the thirteenth year.
Gallows varied wildly, but according to popular lore, 13 steps are leading up to it. Some also associated the number’s unluckiness to 13 menstrual cycles of women based on a 28-day cycle length.
For ancient Persians, history is divided into four chunks of 3000 years. There are variations in the timeframes, but some scholars feel that there will be chaos at the beginning of the 13,000th year as evil mounts a great battle against good (although good will eventually triumph). (click here for more details)