Guides

The Platinum Sequence of Fibonacci Primes

This study combines the logic of Fibonacci numbers with prime numbers and Fibonacci ratios to construct a novel numerical sequence. It was originally published on TradingCenter.org (Giorgos Protonotarios, 2021)

 

By starting with the Fibonacci sequence, next integrating prime numbers, and finally merging both through a state of proportional balance (2.62/6.85).

🏛️ The Fibonacci Sequence – The Foundation

The Fibonacci sequence is a mathematical progression where each term equals the sum of the two preceding terms.

Initial Fibonacci numbers:

0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584, 4,181, 6,765, 10,946, 17,711, 28,657, 46,368, 75,025, 121,393, 196,418, 317,811, 514,229…

Key properties:

• Each term is the sum of the previous two (e.g., 8 = 5 + 3 and 13 = 5 + 8).
• Each number is roughly 1.618 times its predecessor (e.g., 987 ÷ 610 ≈ 1.618) and 0.618 of the next (e.g., 987 ÷ 1,597 ≈ 0.618).

Why Fibonacci ratios matter in global markets

Global markets frequently reach major turning points near Fibonacci numbers and ratios. The 0.618 and 1.618 levels, derived from the golden ratio, are particularly significant in identifying price reversals and retracements.

🌐 Historical Backtesting – Dow Jones Industrial (1928 – 2016)

In my 2018 book ‘Trading World Markets Using Phi and the Fibonacci Numbers’, I analyzed record highs of the Dow Jones Industrial Average between October 1928 and April 2016. The data showed multiple cases where the index achieved new peaks close to Fibonacci numbers.

Results summary:

Out of seven key historical highs, five occurred within 7.5% of a Fibonacci number. Notably, the 1929 and 1966 tops aligned almost perfectly with Fibonacci levels (377 and 987). In every case, the index surpassed the nearest Fibonacci value.

👉 The book: https://www.amazon.com/Trading-World-Markets-Fibonacci-Numbers-ebook/dp/B07KW7H5N4

📝 Prime Numbers – The Building Blocks

A prime number is a natural number that cannot be generated by multiplying two smaller natural numbers. Each has exactly two divisors: 1 and itself.

Initial prime numbers: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89..

Key properties:

• Primes are positive integers greater than 0
• Each can be divided evenly only by 1 and itself
• Prime numbers serve as the fundamental components of all integers

🧮 Constructing the Platinum Sequence of Numbers

The Platinum Sequence is established through three precise steps:

A – Identifying Fibonacci Primes

The process begins by locating numbers that are both Fibonacci numbers and prime numbers.

Within the range from 1 to 1 trillion, only twelve such Fibonacci primes exist.

1 | 2 | 3 | 5 | 13 | 89 | 233 | 1,597 | 28,657 | 514,229 | 433,494,437 | 2,971,215,073

B – Restoring Harmony (2.62 / 6.85)

Although the Fibonacci Primes form a rare subset, the ratios between consecutive members lack consistent proportionality. True numerical harmony is absent.

However, up to 1,597, a pattern emerges showing approximate ratios of 2.62 and 6.85. These values are extensions of the golden ratio (1.618):

• 2.618 = 1.618 × 1.618
• 6.854 = 2.618 × 2.618
• 6.854 = 1.618⁴

👉 Note: The golden ratio (φ) is a universal constant evident in mathematics, architecture, art, music, and natural forms.

C – Completing the Platinum Sequence

The harmony of 1.618, 2.62, and 6.85 serves as the structural foundation. By selectively adding specific Fibonacci numbers, the pattern achieves proportional consistency—creating the Platinum Sequence.

Table: The Platinum Sequence – Fibonacci numbers only

Observations:

• Every element is a Fibonacci number, though not every Fibonacci number is included
• All Fibonacci primes are contained within the sequence
• Numbers in bold (e.g., 89 and 233) represent the twelve Fibonacci Primes
• Additional Fibonacci numbers (e.g., 4,181 and 75,025) are included to restore harmonic balance (2.618 / 6.854)
• The ratios oscillate between 2.618 and 6.854, reflecting a form of natural vibration. According to the Pythagorean school, such oscillation represents the inherent rhythm of the cosmos

Final Insights

After years of applying Fibonacci tools and ratios in trading, their value remains indisputable. The Fibonacci Retracement remains one of the most reliable instruments for identifying key support and resistance zones. Additionally, when the price of an asset enters the so-called “price discovery” phase, Fibonacci Extensions is a unique tool for providing logical targets in higher price levels.

While no tool can predict the future, Fibonacci-based structures offer a lens for identifying proportionality, interpreting volatility, and managing risk-reward relationships. The Platinum Sequence of Numbers, introduced in this work, represents an extension of traditional Fibonacci analysis.

Applying the Platinum Sequence in Financial Markets

The Platinum Sequence can be practically employed across any market by:

• Monitoring significant price highs and lows near its numbers -Extending the concept beyond prices to market capitalizations (price × shares outstanding).
• Watching for possible trend reversals around those levels.
• Treating consecutive closes above or below a sequence number as a signal toward the next harmonic target.

■ Fibonacci Primes – The Platinum Sequence

Concept and calculations by Giorgos Protonotarios, Financial Analyst

for TradingFibonacci.com © -In Cooperation with TradingCenter.org