A Specific Calculating Ability

We report two experiments that investigate the calculating strategy used by a low IQ savant to identify prime numbers. Hermelin and O'Connor (1990) had suggested previously that this subject may use a procedure first described by Eratosthenes to detect a prime number, namely, dividing a target number by all primes up to the square root of the target number and testing for a remainder. In the first experiment, we compare the reaction times of the savant to decide whether a number is prime with those of a control subject proficient in mathematical calculation. In addition, we measured the savant's speed of information processing using an inspection time task. We found that the reaction times of the savant, although generally faster, followed the same pattern of the control subject who reported using the Eratosthenes procedure. The savant's inspection time indicated that his speed of processing was far superior to that expected from someone of his IQ. In the second experiment, we measured the time it takes mathematics students to divide by different prime numbers and we also tested them on the prime identification task. We used their division rimes to simulate their performance on the prime number identification task under the assumption that they used the Eratosthenes procedure. We also simulated the reaction times that would result from a simple memory-based procedure for identifying primes. We found that the Eratosthenes simulation, in contrast to the memory simulation, provided a goad fit to both the students' and the savant's reaction times. We conclude that the savant is using a complex computational algorithm to identify primes and suggest two explanations of how the apparent contradiction between his low general intelligence and his superior numerical ability might be resolved.