| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Prime number conjectures |
| Difficulty | Moderate -0.8 This question requires only routine verification by substitution (checking p=2,3,5,7) and a simple multiplication to show 2^11-1=2047=23×89 is composite. No proof technique or novel insight is needed—just arithmetic and recognizing a counterexample, making it easier than average. |
| Spec | 1.01c Disproof by counter example |
5 (i) Verify the following statement:
$$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p \text { less than } 11 \text { '. }$$
(ii) Calculate $23 \times 89$, and hence disprove this statement:
$$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p ^ { \prime } \text {. }$$
\hfill \mbox{\textit{OCR MEI C3 2008 Q5 [4]}}