Miracles and Evidence Index

By Richard Bruce BA, MA, and PhC in Economics

Former Instructor St. John's University, New York City

## Number Theory studies 666, the number of the Beast.

There have been several comments on this page.

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By Richard Bruce BA, MA, and PhC in Economics

Former Instructor St. John's University, New York City

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 four 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 unusual 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.

I still think that it maybe reasonable to say that God over fulfilled his side of the bet, but perhaps it should be mentioned that as the numbers go up triangular numbers get farther and father away from each other so thinking of this as one in infinity is rather overestimating the situation.

Nevertheless, 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. When Jesus meet the Apostles while they were fishing after the resurrection they caught 153 large fish (John 21:11). There were 120 people in the congregation when a replacement for Judas was chosen (Acts 1:15). Paul's ship that was wrecked on Malta had 276 people on it (Acts 27:37). Finally, the number of the beast is 666 (Revelation 13:18). 120 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, but I did find another source that claimed that these four numbers were the only four three-digit numbers in the New Testament and that they were triangular numbers.

Further research reveals however that there are other three digit numbers. The word hundredfold is used five times. Perhaps that is not exactly a number and is really an estimate, not an exact number anyway. The word hundreds is used once, Mark 6:40. Once again this is not exactly a number and is not an exact number, more of an estimate.

A bit more problematic, the original John 21:8 probably said that Peter's boat was 200 cubits away from shore. Some modern versions would translate this as 100 yards, others as 90 meters, which may explain why it was missed, but in cubits, it would be 200. Cubit is actually from a Latin word that meant a measure from the elbow to the fingertip. It was used by many societies around the Mediterranean. Once again it could be argued that this was just an approximate estimate.

In Revelations 21:17 however there is a number that was no doubt intended to be exact. An angel measures the wall of the heavenly city and determines it is 144 cubits high. Furthermore, revelations says the angel was using the ordinary cubit. So while John 21:17 may have meant about 200 cubits it seems clear that Revelations is referring to the exact standard measure cubit and fully intended the number to be 144. One hundred and forty-four is the square of twelve but is not triangular. Still, we might note that at this point all five numbers with three digits are either triangular or square. Of course, there may be other numbers I have not found.

At an early stage I found this result reasonably impressive. It seemed unlikely that all four numbers with three digits would be 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, but precise math would be beside the point. However the fact that other numbers have been found that do not fit the pattern changes things. This might be an area for further research.

Note that three different books, John, Acts, and Revelation, contain the four numbers. Two different authors, John and Luke, are traditionally given credit for these books. So we would need coordination between these authors to make the pattern work. Interestingly the worst difficulties I have found were in the Gospel of John and the Revelation of John. In fact, the verse about the 200 cubits was three verses before the mention of the 153 fish.

But what is more all the other writers Matthew, Mark, Paul, Peter, James, and Jude must avoid putting a three digit number in their writing. Of course none of these people know that there ever be brought together in the New Testament. Choosing and eventually finalizing the cannon of the New Testament took several hundred years and involved many people. Did all or most know about this pattern, and if they did is it not strange that most scholars have probably been unaware of it.

Another point to note is that three digit numbers stand out to us, but might not stand out in the same way to people who are using Roman Numerals.

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." This is true. I have found more fun stuff myself, and I have found web sites on the Internet that go far more deeply into this than I have.

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 headquarters 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?

Finally, I have a index page with links that lead to many essays providing evidence and defense for the faith.

Tell me what you think. Here is my contact information..

Last edited July 10, 2015Miracles and Evidence Index

**Bible Miracles**

Comments on Bible Names Miracle

The First Supper, Reverses the Last

Death of John the Baptist and Trial of Jesus Reversal

**Catholic Church Miracles**

Evidence the Roman Catholic Church is true church in the name

The gaping difference between popes and bishops points to faith

The Catholic Church was showing respect to women centuries ago few institutions can match today

**Biology Miracles**

The Miracle the Predators so Rarely Eat Us

**Bible Difficulties Resolved**

Explaining the Different Genealogies in Luke and Matthew

Reconciling Matthew's and Luke's Nativity Stories

**Reconciling Science and Religion**

Miracles Contrast with but don't Contradict Science

**Who Believes, Statistics**

List of Catholic Literary Converts

Educated Less Likely to Believe More Likely to Attend

**My Stories**

Conversion through Bible Study, Published in Catholic Digest

Mentioned above My Conversion Through Number Theory

Index of Local Miracle Stories

My Newspaper Article on Local Miracles