• Corpus ID: 231693269

Consecutive primes which are widely digitally delicate

  title={Consecutive primes which are widely digitally delicate},
  author={Michael Filaseta and Jacob Juillerat},
We show that for every positive integer k, there exist k consecutive primes having the property that if any digit of any one of the primes, including any of the infinitely many leading zero digits, is changed, then that prime becomes composite. 

Covering systems with odd moduli

Consecutive primes which are widely digitally delicate and Brier numbers

Making use of covering systems and a theorem of D. Shiu, the first and second authors showed that for every positive integer k , there exist k consecutive widely digitally delicate primes. They also



Digitally delicate primes

Strings of Congruent Primes

In 1920 Chowla made the following conjecture. Let pn denote the nth prime; if q ⩾ 3, (q, a) = 1 then there are infinitely many pairs of consecutive primes pn and pn+1 such that

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A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in 1950, and over the


  • T. Tao
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2011
Abstract We show that for any fixed base a, a positive proportion of primes become composite after any one of their digits in the base a expansion is altered; the case where a=2 has already been

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We answer a question of Erd\H{o}s by showing that the least modulus of a distinct covering system of congruences is no larger than $10^{18}$.

Covering systems with restricted divisibility

. We prove that every distinct covering system has a modulus divisible by either 2 or 3.

Dense clusters of primes in subsets

  • J. Maynard
  • Mathematics, Computer Science
    Compositio Mathematica
  • 2016
It is proved that any subset of the primes which is ‘well distributed’ in arithmetic progressions contains many primesWhich are close together, and bounds hold with some uniformity in the parameters.

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It is shown that the sequence with initial values x0 = 151646890045, x1 = 836564809606, x2 = 942785024683 is the current record in terms of the number of digits.

A New Fibonacci-like Sequence of Composite Numbers

We flnd a new Fibonacci-like sequence of composite numbers and reduce the current record for the starting values to A0 = 106276436867 and A1 = 35256392432. In this note we consider Fibonacci-like