The data on this page is associated with the paper "Consecutive primes which are widely digitally delicate" by Michael Filaseta and Jacob Juillerat. There are two main lists to aid with following the constructions in the paper:
(i) a list of positive integers m and the primes p for which the order of 10 modulo p is m , and
(ii) a list that for the covering systems presented in tables in the paper.
Details regarding these lists are written below.
(i) a list of positive integers m and the primes p for which the order of 10 modulo p is m ,
Each element of this list is itself a list of the form [m,[p_1,...,p_t]]. The first entry m indicates that what follows is describing primes p for which the order of 10 modulo p is m. The m correspond to the moduli used in covering systems in the paper. In each case, p_1 < p_2 < ... < p_{t-1} and either p_{t-1} < p_{t} or p_{t-1} = p_{t}. If p_{t-1} < p_{t}, then the numbers p_1,...,p_{t-1} are distinct primes p for which the order of 10 modulo p is m. In this case, p_{t} is either a prime p for which the order of 10 modulo p is m or a composite number whose prime factors p are distinct from p_1,...,p_{t-1} and each prime factor p has the order of 10 modulo p equal to m. If p_{t-1} = p_{t}, then the numbers p_1,...,p_{t-2} are distinct primes p for which the order of 10 modulo p is m and p_{t-1} = p_{t} is a composite number which is not a power of a prime and which is relatively prime to the product of the primes p_1,...,p_{t-2}. Each prime divisor of p_{t} is such that the order of 10 modulo that prime is equal to m. These primes are determined by factoring or partially factoring Phi_{m}(10), where Phi_{m}(x) is the m-th cyclotomic polynomial. The list [m,[p_1,...,p_t]] is indicating that there are at least t primes for which 10 has order m modulo p .
Click here for a text file of this list of prime divisors of Phi_{m}(10).
(ii) a list that for the covering systems presented in tables in the paper.
This is a series of lists, one for each value of d in {-9, -8, ..., -2, -1} union {1, 2, ..., 8, 9}. The list corresponding to d is called table[d] and gives the information for a table associated with d in the paper. Each table is written as a list of lists of the form [a,m,p] corresponding to the congruence k = a (mod m) where p is a prime (or composite, but then p is associated with a prime divisor of this composite number) and m is the order of 10 modulo p. In other words, p appears in the list in (i) above for m. As above, p may appear twice (and hence m twice) if p is composite with at least two distinct prime factors. If q_1 and q_2 are two distinct prime factors of p in this case, then they are prime factors of Phi_{m}(10) which are relatively prime to m and hence 10 has order m modulo each of the primes q_1 and q_2. Thus, in the case that p is composite, the interpretation of [a,m,p] is that the congruence represented is k = a (mod m) and the prime p is one of q_1 and q_2, where each of these primes can be used with a different value of a.
Click here for a text file of lists of these tables.