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A conjecture is an unproven statement based on observations of a pattern. It is an educated guess that holds true for many supporting cases. A conjecture about the sum of any three consecutive numbers, for example, is shown in the table.
| Sum of Any Three Consecutive Integers | ||
|---|---|---|
| Observation I | Observation II | Observation III |
| 2+ 3+4& =9 & =3* 3 | 7+ 8+9& =24 & =3* 8 | 13+ 14+15& =42 & =3* 14 |
| Conjecture: The sum of any three consecutive integers is three times the second number. | ||
However, it is unknown whether any given conjecture holds true for all cases. It could be false under some circumstances and, therefore, cannot be used to support other claims. A counterexample is enough to prove that a conjecture is false. When a conjecture is rigorously proved, it becomes a theorem.
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Goldbach's Conjecture |
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Every even whole number greater than 2 is the sum of two prime numbers. |
For example, the even numbers below follow the rule. 14 & = 3+ 11 24 & = 11+13 40 & = 17+23 As of 2013, the conjecture has been verified by a computer for all integers less than 4 * 10^(18). In March 2000, it was announced that anyone who could prove Goldbach's Conjecture and whose proof was accepted by other mathematicians would be awarded a one million dollar prize. Although the prize was kept open for two years, nobody claimed it.