Chart 1

 Chart 2

Benford's law

, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale. Benford's law also gives the expected distribution for digits beyond the first, which approach a uniform distribution as the digit place goes to the right.

This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws, which are very common in nature. It tends to be most accurate when values are distributed across multiple orders of magnitude. Benford’s law is used to detect fraud. In this instance it highlights discrepancy in data, read further for explanation. There is plenty of information on the web if one is interested, just google search for Benford’s law.

Now this law has been applied to the numeric codes of the Quran.  Above there are two graphs blue series is a model graph of how Benford’s law should appear.  Green series is the graph made for the codes.  Briefly codes are from the Quran and are above hundred in all.  The criteria to create these Code’s is simple, geometric values of six messengers are either concatenated or added to either the verse or the verse and the chapter number where the word messenger is referred or implied.  These messengers are Quran, Torah, Gospel (Injeel), Muhammad, Rashad Khalifa and Al-Muzzammil.  When these codes are divided by 19 we get complete multiple of 19.  There is plenty of information on this web site about the codes including FAQ’s, please read in your own time.

However, for the purpose of this article we should concentrate the application of Benford’s law and the graphs above.  As you can see the first graph is in a shape of a slope and the second graph for the codes starts as a slope but further down has two peeks.  From this observation we can say that the second graph follows Benford’s law for all digits except 5 and 9.

First since in general the second graph follows Benford’s law is another proof that these codes are authentic and true.  There are other proofs for the authenticity of the codes like “Position and Level”, cyclic Groups and Calculus which also apply to these codes.  Once again these proofs are for your reading on this web site.

The unusual behaviour of 5 and 9 to peek can be explained.  Digit 5 is starting digit for the geometric value of Rashad in Arabic and 9 is a starting digit for the geometric value of Muhammad in Arabic.  And the value’s of this graph has been calculated by adding first digit of every code.  Now why did these two peek?

The Benford’s law does not work for the digits which have discrepancies.  For example budget figures when messaged do not hold fast the Benford’s law.

Thus keeping this in mind we can explain the discrepancy with the two peeks.  The discrepancy is that both Muhammad and Rashad are both were messengers but are not now, since they are both dead.  And this graph is of the messengers.

Thus the Benford’s law worked to its best and showed the consistency and non-consistency in the same graph.