Are Prime Numbers Good Lottery Numbers?

Edvin Hiltner
8 min readMar 15, 2021

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Using prime numbers in lottery games is one strategy some players follow. This article will explore whether prime numbers work as a lottery strategy.

Playing the lottery involves picking some numbers out of a number pool. For example, the Florida Lottery Fantasy 5 playable combination has five numbers from 1 to 36.

This is a crucial moment for players, so they follow a strategy to pick the most auspicious numbers. Some players create a combination containing all prime numbers. Some people observe prime numbers appear more frequently than other numbers in lotteries.

A prime number is a natural number greater than one whose factors are one and itself. For example, 2 is a prime number because its factors are 1 and 2. Another prime number is 3 because its factors are 1 and 3.

The first 25 prime numbers less than 100 are:

In the playslip of Florida Fantasy 5, you can make a vertical pattern with the 5th column in the matrix. The first five numbers in this column are all prime numbers. Thus, you can create a geometric lottery pattern containing prime numbers.

However, this strategy is not recommended; you will find the reasons below.

The Search For an Effective Lottery Tool

Winning the lottery is truly a challenge. With the randomness of a lottery draw, everyone can only predict the next winning numbers.

Hence, every lotto player must plan how to play a game. Thus, you need to understand the nature of a lottery draw. Even though the lottery is truly random, it is also mathematically deterministic. You will never know the next winning combination, but you can see its predetermined future behavior based on the law of large numbers.

In a lottery game, every ball in the urn has the same shape, size, texture, and weight. There is no influencing factor that will make some numbers more favored than others numbers. Every ball has an equal chance of being picked.

Some numbers are more frequently drawn if we are talking about the first 50 or 100 draws. With more draws held, other less frequently drawn numbers will soon catch up.

Thus, you can no longer see hot and cold numbers through statistics of past draws. Similarly, you can no longer claim that prime numbers are drawn more frequently than others.

Here are the bubble charts for Florida Lottery Fantasy 5 number frequency.

The data used for these charts are from 7,181 draws since July 16, 2001. Notice that all sections (representing numbers) have similar sizes.

So, if statistics of hot, cold, and prime numbers do not offer an effective game plan in lotteries, what does?

Let’s take a look at this image below:

Source: A Visual Analysis of a Truly Random Lottery with a Deterministic Outcome

This image of the lottery’s true randomness suggests ideas you can use to play lotteries strategically. The dots and streaks in this image represent the number of times a combination has occurred.

See the dark gray dots? You must use these combinations to gain the upper hand in the game.

The upper hand does not mean you will know the next winning combinations. Instead, you will know how to play with more favorable opportunities to win. This is possible through the help of probability theory along with combinatorial mathematics. (Read The Winning Lottery Formula Based on Combinatorics and Probability Theory)

The Difference Between Probability And Odds

Probability is what we use to measure the likelihood of a certain event. To do this, we use the following equation:

Comparing the number of favorable combinations with the total combinations gives the probability of winning. In the Florida Fantasy 5, there are 376,992 total combinations.

Suppose you wish to play with 1–2–3–4–5. The probability of winning from this combination is 1 in 376,992. Each of the remaining 376,991 combinations offers the same probability. Mathematically, buying more combinations is the only way to increase your probability of winning.

However, you might buy as many combinations as you can afford. But there’s the possibility that you’ll buy more combinations and waste money in the process because you don’t get the best favorable shots possible.

A smart player will not buy just any combination. Instead, he will spend money on the most favorable combinations.

To know which combinations are most favorable, we must deal with the concept of odds.

We use odds to measure the ratio of success to failure. To do that, we use the following equation:

The basic terms you must know as a lottery players are numbers and combinations. In Fantasy 5, You have to combine five numbers to make a combination and play. The number field can be grouped into four sets:

Odd = {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35}

Even = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36}

Low = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}

High = {19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36}

Therefore, combinations can have varying compositions of odd, even, low, and high numbers. Since combinations have different compositions, different combinatorial groups with varying ratios of success to failure exist.

The most auspicious combinations belong to the group with the best success and failure ratio. To know what these combinations are, we need to use the tools of combinatorics and probability theory.

Combinatorial and Probability Analysis For Odd and Even Numbers

A Lottery’s number field has odd and even numbers. In Florida Fantasy 5, you can create all the 376,992 combinations with the following odd/even patterns.

Source: How to Win the Lottery According to Math

As the table above shows, each combinatorial group has varying probability values. Noticeably, you get less favorable shots when you combine numbers where all numbers are odd or even numbers. For example, combining five even numbers gives you two favorable shots in 100 attempts. The same holds for a combination where all numbers are odd.

The table shows that the best choices are 2-odd-3-even or 3-odd-2-even, while the worst choices are 5-even or 5-odd.

There are more combinations out of 3-odd-2-even and 2-odd-3-even, and therefore, according to probability theory, winning combinations will come from these groups more often.

Looking at the table of prime numbers above, this Fantasy 5 game contains only 11 prime numbers. These are 2, 3, 5, 7, 11, 13,17,19,23, 29 and 31.

Following the prime numbers strategy, you could use two possible patterns. These are 1-even-4-odd or 5-odd. Based on the combinatorial analysis, these patterns don’t belong to the best groups. Therefore, focusing too much on prime numbers and neglecting others will not give you the best shot possible.

Your job as a lotto player is to make a combination that will give you more favorable shots. In this case, you should choose either 3-odd-2-even or 2-odd-3-even. Each combinatorial group will give you 33 favorable shots out of 100 attempts.

When you choose a 1-even-4-odd combination where four numbers are prime, you get only 15 favorable shots out of 100 attempts.

Similarly, when you play with 5-odd numbers where all are prime numbers, you get only two favorable shots out of 100 attempts.

As a lotto player, consider balancing your odd and even numbers to get the best ratio of success to failure.

Always go for combinatorial groups with the best ratio of success to failure.

There is no way to change the probability of a lottery game. There is also no way you can easily defeat its odds. Nonetheless, you have the power to know which combinatorial group have the best ratio of success to failure. You can make the most logical choice. In fact, you may choose not to play lotto if you think the odds are too monumental to beat.

Advanced Combinatorial Analysis to Find the Best Combinations

When you analyze your game based on odd and even numbers, you get the idea that some combinations get more favorable shots even though every combination has the same probability.

However, a lottery’s number field doesn’t involve odd and even numbers. Part of the analysis must also include the low and high numbers.

If we neglect the low and high numbers, we might face a little contradiction.

For example, 1–2–3–4–5 is considered best under odd/even analysis. Still, we know it belongs to the worst group under the low/high analysis simply because most winning combinations tend to have a balance of low and high numbers.

To prevent contradiction, we have to combine odd/even and low/high analysis into one combinatorial and probability. Therefore, we have to use the Lotterycodex method.

In Lotterycodex, we divide the lottery’s number field into four sets:

Source: The Winning Lottery Formula Based on Combinatorics and Probability Theory

The above image is the Lotterycodex combinatorial design for a 5/36 game. Notice that the odd, even, low, and high numbers have been regrouped. The numbers are found in low-odd, low-even, high-odd, and high-even sets.

The above sets ensure that the probability and combinatorial analysis will consider all four groups of numbers, thereby avoiding all contradictory conclusions.

The four sets will produce three groups of Lotterycodex patterns:

Fantays 5/36 lotterycodex patterns are divided into three groups. The best patterns are from pattern #1 to #4. The middle patterns are from patterns #5 to #26. The worst patterns are from patterns #29 to #56.
Source: Lotterycodex Calculator

As you can see from the image above, the best Lotterycodex patterns for a 5/36 game are patterns #1, #2, #3, and #4.

Math calculations can be very complex. If you hate math, then you can use a Lotterycodex calculator to deal with the complexity. (See Lottery Calculator: Knowing the Best Lotto Combinations Without a Math Degree)

Through advanced Lotterycodex combinatorial and probability analysis, you will be compelled to use numbers other than prime numbers so that the ratio will surely improve.

You will know which combinations are the best and the worst. As a lotto player, your job is to get the best shot possible.

Many players do not know that the combinations they have been using for years will only give them one favorable shot after 100 attempts, and that’s an expensive strategy. Lotterycodex combinatorial analysis can prevent you from playing blindly and wasting money on a group combination that will take years to get favorable opportunities to match the winning combination.

Take a look at the table below.

Source: Lotterycodex Calculator

The best patterns will give you the maximum number of favorable opportunities for winning.

Expected Occurrences of Pattern #1
= 0.0696142093 x 2,000
= Occurs about 139 times in 2000 draws

Expected Occurrences of Pattern #17
= 0.0180481283 x 2,000
= Occurs about 36 times in 2000 draws

Expected Occurrences of Pattern #53
= 0.0003342246 x 2,000
= Occurs about once in 2000 draws

The best pattern will always dominate the game. This is what the law of large numbers states and shall be fulfilled as more draws are held. The table above shows that even in 5,000 draws, pattern #1 will remain ahead of the middle and worst patterns.

If you like to use prime numbers, then add prime numbers in your combinations. But also remember to include non-prime numbers to ensure balance.

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Edvin Hiltner

Edvin Hiltner runs Lotterycodex.com to prove that a sensible lotto strategy is practically feasible through the use of mathematics.