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Number Theory studies 666, the number of the Beast.


I believe it was 1981, or maybe late 1980 when I started to study Newton's writings on the Book of Revelation. The Anchor Bible commentary series had a little note in it that said that 666, the famous number of the beast from revelations, was a triangular number. A triangular number is like a square except you arrange the dots in an equilateral triangle rather than a square. For example, the ten pens in bowling are arranged into a triangle with three pens on a side. An equilateral triangle with 36 dots on a side would have 666 dots in all.

I noted that 6 was the triangle of 3, and so I checked to see if 66 was a triangular number. It is, 66 is the triangle of 11. So 6, 66, and 666 are all triangular numbers, and as it turns out longer strings of 6, 6,666, and 66,666 etc. are not triangular numbers.

I wondered how rare this is and after checking 1, 2, 3 on up to 9 in base 10, which is our normal base, I tried to get more data by checking other bases. I looked at numbers where all the digits were 1 in base 2, where all digits were 1, or all were 2 in base 3 and so on up to about base 20.

Having done this I wondered if this would interest the number theorists in the math department. I was told that the Math Department at UC Davis had two number theorists, the more distinguished happened to be out so I gladly went to the number two man. As it turned out a former child prodigy, who by this time was 21 and had a PhD in Math, happened to be in the office, and he was interested in number theory and my project.

The prodigy found out that any series of identical digits was triangular if the base was eight times the digit plus one. For example 1, 11, 111, 1,111, 11,111 etc. are triangular in base nine, one times eight plus one equals nine. Similarly 3, 33, 333 etc. were triangular in base 25. But only 6 in base 10 works for the first three numbers but not the rest.

The prodigy wrote a computer program to test the proposition for a hundred thousand cases or more, but he could not prove it that this property of 6 and base ten was unique with a computer. So he tried to find a mathematical proof, but that proved to be difficult. A math professor at St. John's University, where I taught several years later, also became interested in the problem, but he could not find a proof either.

This happened decades ago in the early and mid eighties, but more recently I got information from the prodigy that the problem was being considered for publication in the latest edition of an academic book. After a number of months or perhaps a year I contacted the professor who was writing the book in question and apparently the problem was not included in his book.

Still all of this greatly impressed me back in the 1980's. I had been investigating the issues of faith, particularly Christianity anyway, that is why I was studying Revelations in the first place. I had mentally made one of those typical wagers with God, I would go to church if the relationship between triangular numbers and 666 proved to be unusual. I thought maybe on in a hundred or one in a thousand was unusal enough. When the former prodigy told me it was probably one in infinity, I figured that God had over fulfilled his side of the bet.

What also impressed me was that an academic publication might come out of it. After all I had only had about five minutes training in number theory. I was taking an undergraduate class on modern algebra and the teacher decided to do a brief digression on number theory. He taught us in a rudimentary way what number theory was. Based on that I had started a project that might lead to an academic publication. I thought that was impressive and easily enough to get me to go to church.

As I went along I found other things to base my faith on, and the skeptic would be justified in saying I was probably headed to Church anyway, but this is one part of my story.


There have been several comments on this page.

One comment claimed that all four of the numbers which have three digits in the New Testament are triangular. There were 120 people in the congregation when a replacement for Judus was chosen (Acts 1:15). When Jesus meet the Apostles while they were fishing after the resurection they caught 153 large fish (John 21:11). Paul's ship that was wrecked on Malta had 276 people on it (Acts 27:38). Finally, the number of the beast is 666 (Revelation 13:18). One hundred twenty is the triangle of 15, 153 is the triangle of 17, 276 is the triangle of 23, 666 is the triangle of 36.

I have not read back through the whole of the New Testament to check this, I just got the message in June 2008. I also do not know what the original source of this is.

What is the chance of all four numbers with three digits being triangle numbers given the size of these numbers. For a very rough guess we could multiply the four roots, 15, 17, 23, and 36. This would give us very roughly one in two hundred thousand. This is not presented as rigorous or precise math.

Another person wrote and said, "Interesting. I don't like numerology but check Second Chronicles 9:13 and Wisdom, Solomon." I did not check out the whole of Wisdom. But the reference in Second Chronicles 9:13 says that Solomon got 666 talents of Gold in one year.

Another person wrote, "666 has many more extremely interesting characteristics."


You can read another part of my story in My Conversion to the Catholic Church through Bible study. This was originally published in Catholic Digest, which is probably the most read Catholic periodical in the English language.

The 666 triangle pattern is not the only time I have found interesting patterns in the Bible, or even the only one that impressed professors and other experts. When Old and New Testament figures share the same name the Old Testament stories foreshadow the New in miraculous ways.

This has impressed a distinguished professor at the Graduate Theological Union in Berkeley, Wilhelm Wuellner and Gerry Matatics, a friend of Scott Hahn who tried to prevent him from joining the Catholic Church and ended up joining himself.

Monarchs and other autocrats, like Hussein and the present leadership of China, hate to share the loyalty of their subjects with religious leaders they can not execute. Therefore they try to break up centrally organized religions when the head quarters is outside their country. Thus it has been very difficult to for any highly centralized religion to maintain the loyalty of the majority of even two independent countries, yet the Catholic Church has maintained the loyalty of the majority of dozens of countries for many centuries. Is this a miracle?


In addition to my playing around with 666 and number theory I have also done some speculation in other areas that the University of California at Davis professors found impressive. Here is a hypothesis on why whales are so large compared to land animanls. The underlying theory impressed several biology profs who said it should be submitted to an academic journal.

You can leave one or more notes in my guest book. Do not write much beyond the little box they give you, they will simply cut off the last part or your message, just put a second and as many messages as you need in the guest book. If you leave an e-mail I will usually contact you.

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