منابع مشابه
A Probable Prime Test with High Confidence
Monier and Rabin proved that an odd composite can pass the Strong Probable Prime Test for at most 1 4 of the possible bases. In this paper, a probable prime test is developed using quadratic polynomials and the Frobenius automor-phism. The test, along with a xed number of trial divisions, ensures that a composite n will pass for less than 1 7710 of the polynomials x 2 ? bx ? c with b 2 +4c n = ...
متن کاملRepunit R49081 is a probable prime
The Repunit R49081 = (1049081 − 1)/9 is a probable prime. In order to prove primality R49080 must be approximately 33.3% factored. The status of this factorization is included. Repunits are numbers of the form Rn = (10 − 1)/9. Considerable computer time has been spent factoring repunits, creating interesting primes based on the characteristics of repunits, and searching for repunit primes. One ...
متن کاملAverage Case Error Estimates for the Strong Probable Prime Test
Consider a procedure that chooses fe-bit odd numbers independently and from the uniform distribution, subjects each number to t independent iterations of the strong probable prime test (Miller-Rabin test) with randomly chosen bases, and outputs the first number found that passes all t tests. Let pfc , denote the probability that this procedure returns a composite number. We obtain numerical upp...
متن کاملThe Probability that a Random Probable Prime is Composite
Consider a procedure which (1) chooses a random odd number n < x, (2) chooses a random number 6, 1 < b < n — 1, and (3) accepts n if bn~l = 1 (mod n). Let P(x) denote the probability that this procedure accepts a composite number. It is known from work of Erdös and the second author that P(x) —> 0 as x —► oo. In this paper, explicit inequalities are established for P(x)\ For example, it is show...
متن کاملFurther investigations with the strong probable prime test
Recently, Damg̊ard, Landrock and Pomerance described a procedure in which a k-bit odd number is chosen at random and subjected to t random strong probable prime tests. If the chosen number passes all t tests, then the procedure will return that number; otherwise, another k-bit odd integer is selected and then tested. The procedure ends when a number that passes all t tests is found. Let pk,t den...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 1995
ISSN: 0899-6180
DOI: 10.35834/1995/0703132