Primorials

Posted By on Mar 22, 2018 | 0 comments


The primorial numbers emerge from the fractions that Emily calculates. The primorials form an integer sequence which is created by multiplying successive prime numbers.

The first in the sequence is the first prime number:

    \[2\]

The second in the sequence is:

    \[2 * 3 = 6\]

The third is:

    \[2 * 3 * 5 = 30\]

Then:

    \[ 2 * 3 * 5 * 7 * 11 = 2310 \]

    \[ 2 * 3 * 5 * 7 * 11 * 13 = 30030 \]

    \[ 2 * 3 * 5 * 7 * 11 * 13 * 17 = 510510 \]

    \[ 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = 9699690 \]

And so on. The numbers get quite big, very quickly.

The term ‘primorial’ was created by Harvey Dubner, combining ‘prime’ with ‘factorial’. The factorial sequence (A000142) is found by multiplying successive integers:

    \[ 1 \]

    \[ 1*2=2 \]

    \[ 1*2*3=6 \]

    \[ 1*2*3*4=24 \]

    \[ ... \]

Harvey was a prolific hunter of large prime numbers and invented computing equipment that helped to multiply numbers at great speed.

Harvey Dubner also contributed the High-Low Ratio to the world of blackjack. It is a method of estimating the best bet based on the cards that have been dealt previously. Jerry Patterson describes a first-hand account of the 1963 Las Vegas conference where Harvey first presented his method in ‘The Forgotten Man of Blackjack’. A brief description of Harvey’s career can also be found in the book ‘Never Split Tens’.

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