The Fibonacci and Lucas number sequences have intrigued amateur and professional mathematicians for centuries. The Fibonacci sequence begins with 0, 1 whilst the Lucas sequence begins with 2, 1. After that, the next integer in either sequence is simply found by adding the previous two numbers.

These numbers are closely related to the golden ratio. By dividing a number in either sequence by its predecessor, an approximation of the golden ratio, phi or φ is achieved. The higher the numbers, the more precise the approximation. It can never be exact because phi is an irrational number, which means it cannot be expressed as any two integers a/b.

For example, 5778 / 3571 = 1.618034... which is very close to the exact value of phi which is (1 + √5) / 2. Note that phi, the golden ratio, is not to be confused with Euler's totient function. Although both use the same Greek symbol φ, they are unrelated functions.

5778 is the sum of four consecutive Fibonacci numbers (...610, 987, 1597, 2584...), but what makes 5778 special is that despite an infinite number of Lucas numbers, it has been proven that only three of these are also triangular. Those numbers are 1, 3 and 5778. Remarkably, phi raised to the 18th power equals 5778.

• L(18) = 5778
• φ¹⁸  =  5778
• 5778 = 18 x 321

The significance of number 18 can be appreciated when the 5778 triangle is deconstructed into 18 segments. 

It can be seen that the Genesis 1:1 triangle (and its constituent parts) together with the mysterious triangular number 153 figure prominently in the 18 piece 5778 jigsaw. The overall picture is a tolerable illustration of the miraculous catch of fish outlined in John 21. The three pieces representing the sky total 1998, which is the gematria value of  "In the beginning God created the heaven..." from Gen 1:1, whilst the 1088 trapezium (the boat upon the waters) matches the gematria value of Psalm 145:17.

                                                "The LORD is righteous in all his ways, and holy in all his works"
                                            צדיק  יהוה  בכל  דרכיו   וחסיד  בכל  מעשיו                    
                                                    426             52             88                 240            52           26           204        =      1088

• 153 x 13 = 1989
• mass of the sun = 1.989 x 10³⁰ kg

Notice how the key numbers from the 5778 triangle all reduce to 9:

• 5 + 7 + 7 + 8 = 27, and 2 + 7  =  9
• sky = 6 + 6 + 6 = 18, and 1 +  8  =  9
• water = 1 + 5 + 3  =  9
• boat = 1 + 0 + 8 + 8 + 7 + 0 + 3  =  27,  and  2 + 7  =  9
• Psalm 145:17 gives 1 + 4 + 5 + 1 + 7  =  18,  and  1 + 8  =  9
• sky - water  =  1998 - 1989  =  9
• John 21:11 gives 21/11 = 1.9090909...

Without doubt, 5778 is an important gematria number. Of particular interest is that 5778 on the Hebrew calendar coincides with 2017-2018 on the Gregorian calendar.

The Hebrew year 5778 coinciding with 2018 on the Gregorian calendar is significant, as it was in the year 2018 AM that God made the first covenant with Abraham. (AM = Anno Mundi, or years since creation). This was 70 years after Abraham's birth in 1948 AM. The new independent state of  Israel was established in 1948 Gregorian, so 2018 will also be 70 years (or a generation, see Psalms 90:10) since then.

"The days of our years are threescore years and ten; and if by reason of strength they be fourscore years..."  Ps 90:10a

"Verily I say unto you, This generation shall not pass, till all these things be fulfilled." Mat 24:34

• φ¹⁸  =  5778
• 5778 is the 107th triangular number.
• There are 107 verses spoken by Jesus in the sermon on the mount. (Matthew 5:3 - 7:27)

• surface temperature of the sun = 5778˚ K

The Hebrew word for mankind is spelled ADM, which many kabbalists say is an acronym for Adam - David - Moshiach. King David was born in 907 BCE, which is 2854 on the Hebrew calendar. David is the comprehensive soul of all mankind, and is the forerunner of Moshiach, who brings about redemption for all mankind. David lived for 70 years, so the midpoint of his life was in the 2889th year since creation. This year was also half way towards the year 5778!

It is said that Adam was created to live for 1,000 years, but gifted King David 70 years of  his life (Zohar 1, 55a). Together, the years of the lives of Adam (930) and David (70) sum to the 1,000 years of the Messianic era (the millenium). You can read more about the significance of 5778 at  kabbalahsecrets.com.

We have seen how 1776 can be organized into three pairs of Roman numerals, separating the numbers 1110 and 666 which form  a Pythagorean triangle with 888.

Simply multiplying those numbers by three makes for an intriguing study:

"The New Jerusalem was an important theme in the Puritan colonization of New England in the 17th century. The Puritans were inspired by the passages in Revelation about the New Jerusalem, which they interpreted as being a symbol for the New World. The Puritans saw themselves as the builders of the New Jerusalem on earth. This idea was foundational to American nationalism." - Wikipedia

Read more about the notion that America was the New Jerusalem from the PBS Frontline program  "Apocalypticism Explained - The Puritans".

According to the sages, Messiah must come (return) no later than 6000 years since creation. It can be sooner, but no later than this date. This is in keeping with the Sabbath pattern - 6000 years since creation followed by 1000 years of the millennium. A thousand years are equivalent to one day in the eyes of God, as is written in Psalms (90:4).

The Talmud (b.Avodah Zarah 9a) states the following:

        "The world is to exist for six thousand years; the first two thousand years are to be void; the next two thousand years
         are the period of the Torah, and the following two thousand years are the period of the Messiah."

The first letter of the Hebrew alphabet (aleph) can also be pronounced eleph, which means "thousand" and in Hebrew is spelled אלף which
has a millui (spelled out) gematria value of  1 + 30 + 80 = 111 (3 x 37). So six alephs have a literal and a numerical meaning:

• literal meaning = 6 x 1,000 = 6,000
• millui gematria value = 6 x 111 = 666

For sure, man's number is up after 6,000 years! A further clue can be found in Genesis 1:1, who's 28 Hebrew letters include 6 alephs. These six alephs occupy letter numbers 3, 9, 10, 15, 23, and  26 of  Genesis 1:1, and the sum of these numbers is 86, the gematria of Elohim (אלהים), the third word from Gen 1:1.