06-21-2026, 01:52 PM
[font=-apple-system, '.SFNSText-Regular', 'San Francisco', Roboto, 'Segoe UI', 'Helvetica Neue', 'Lucida Grande', Arial, sans-serif]Richert Theorem[/font]
Summary
Richert’s Theorem, proved by Hans-Egon Richert in 1948, states that every integer greater than or equal to 7 can be expressed as a sum of distinct prime numbers. The article presents a short proof based on Bertrand's Postulate, which guarantees a prime between any number (n) and (2n).
Starting from the fact that all integers from 7 to 19 can be written as sums of distinct primes from (${2,3,5,7,11}$), the proof uses induction and the inequality $(p_{i+1}<2p_i)$ to show that increasingly larger intervals of integers can also be represented as sums of distinct primes. By extending these intervals indefinitely, it follows that every integer ($n\ge 7$) has such a representation, illustrating a beautiful connection between prime distribution and additive number theory.
ARTICLE
Summary
Richert’s Theorem, proved by Hans-Egon Richert in 1948, states that every integer greater than or equal to 7 can be expressed as a sum of distinct prime numbers. The article presents a short proof based on Bertrand's Postulate, which guarantees a prime between any number (n) and (2n).
Starting from the fact that all integers from 7 to 19 can be written as sums of distinct primes from (${2,3,5,7,11}$), the proof uses induction and the inequality $(p_{i+1}<2p_i)$ to show that increasingly larger intervals of integers can also be represented as sums of distinct primes. By extending these intervals indefinitely, it follows that every integer ($n\ge 7$) has such a representation, illustrating a beautiful connection between prime distribution and additive number theory.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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