From Moses to the Second Temple Only Nine Red Heifers
Parsha Pages Youth | July 08, 2024
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From Moses to the Second Temple Only Nine Red Heifers

Parsha Pages Youth | June 27, 2025

The Tenth Red Heifer Will be Prepared by the King Moshiach

ויקחו אליך פרה אדמה (יט, ב)verse in this section)
“Take unto you a red heifer” (1st verse in this section)
Only to you, Moshe, and not to anyone else
Even Shlomo HaMelech, the wisest man in the world, could not decipher the logical secret.

לטמא מאפר שרפה החטאת (יט, יז) (last verse in this section)
This Parsha was given to TO MOSHE (heads of letters in direct order) and NOT to SHLOMO (same letters but out of order)

קוהלת ז, כג כָּל-זה, נִסִיתִי בַחָּכְמָּה; אָּמַרְ תִי אֶחְכָּמָּה, וְהִיא רְ חוֹקָּה מִמֶנִי.
"I will be wise, but it was far from me” (written by ShlomoHaMelech)

והיא רחוקה (341) פרה אדומה

MATHTOID

341 is the smallest pseudoprime in base 2
A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy.
The most important class of pseudoprimes come from Fermat's little theorem and hence are called Fermat pseudoprimes. This theorem states that if p is prime and a is coprime to p, then ap-1 - 1 is divisible by p. If a number x is not prime, a is coprime to x and x divides ax-1 - 1, then x is called a pseudoprime to base a. A number x that is a pseudoprime for all values of a that are coprime to x is called a Carmichael number.
The smallest Fermat pseudoprime for the base 2 is 341. It is not a prime, since it equals 11 · 31, but it satisfies Fermat's little theorem: 2340 ≡1 (mod 341).

The rarity of such pseudoprimes has important practical implications. For example, public-key cryptography algorithms such as RSA require the ability to quickly find large primes. The usual algorithm to generate prime numbers is to generate random odd numbers and test them for primality. However, deterministic primality tests are slow. If the user is willing to tolerate an arbitrarily small chance that the number found is not a prime number but a pseudoprime, it is possible to use the much faster and simpler Fermat primality test.

Which of the following also equal 341?

  • זה על עון עגל
  • איננה טהורה
  • כל ארץ
  • כף הירך
  • בשיבה טובה
  • לאיש

The Tenth Red Heifer Will be Prepared by the King Moshiach

ויקחו אליך פרה אדמה (יט, ב)verse in this section)
“Take unto you a red heifer” (1st verse in this section)
Only to you, Moshe, and not to anyone else
Even Shlomo HaMelech, the wisest man in the world, could not decipher the logical secret.

לטמא מאפר שרפה החטאת (יט, יז) (last verse in this section)
This Parsha was given to TO MOSHE (heads of letters in direct order) and NOT to SHLOMO (same letters but out of order)

קוהלת ז, כג כָּל-זה, נִסִיתִי בַחָּכְמָּה; אָּמַרְ תִי אֶחְכָּמָּה, וְהִיא רְ חוֹקָּה מִמֶנִי.
"I will be wise, but it was far from me” (written by ShlomoHaMelech)

והיא רחוקה (341) פרה אדומה

MATHTOID

341 is the smallest pseudoprime in base 2
A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy.
The most important class of pseudoprimes come from Fermat's little theorem and hence are called Fermat pseudoprimes. This theorem states that if p is prime and a is coprime to p, then ap-1 - 1 is divisible by p. If a number x is not prime, a is coprime to x and x divides ax-1 - 1, then x is called a pseudoprime to base a. A number x that is a pseudoprime for all values of a that are coprime to x is called a Carmichael number.
The smallest Fermat pseudoprime for the base 2 is 341. It is not a prime, since it equals 11 · 31, but it satisfies Fermat's little theorem: 2340 ≡1 (mod 341).

The rarity of such pseudoprimes has important practical implications. For example, public-key cryptography algorithms such as RSA require the ability to quickly find large primes. The usual algorithm to generate prime numbers is to generate random odd numbers and test them for primality. However, deterministic primality tests are slow. If the user is willing to tolerate an arbitrarily small chance that the number found is not a prime number but a pseudoprime, it is possible to use the much faster and simpler Fermat primality test.

Which of the following also equal 341?

  • זה על עון עגל
  • איננה טהורה
  • כל ארץ
  • כף הירך
  • בשיבה טובה
  • לאיש
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