Prime birthdays on prime years

Code.js

const THIS_YEAR = 2017;
const MAX_AGE = 123;

// https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
function sieveOfErathosthenes(max) {
  const notPrimes = [];
  const top = Math.sqrt(max);
  const primes = [];

  for (let i = 2; i < top; i += 1) {
    if (!notPrimes[i]) {
      for (let j = i * i; j < max; j += i) {
        notPrimes[j] = true;
      }
    }
  }

  for (let i = 2; i < max; i += 1) {
    if (!notPrimes[i]) primes.push(i);
  }
  return primes;
}

const primes = sieveOfErathosthenes(THIS_YEAR + MAX_AGE);

// For all years starting a century+ ago ...
for (let yearOfBirth = THIS_YEAR - MAX_AGE; yearOfBirth <= THIS_YEAR; yearOfBirth += 1) {
  let headingPrinted = false;
  let age = 1;
  let total = 0;
  let sets = 0;
  // for all ages below the maximum
  while (age < MAX_AGE) {
    // Check whether both the age and the year are prime numbers
    const indexYear = primes.indexOf(age + yearOfBirth);
    const indexAge = primes.indexOf(age);
    if (indexYear !== -1 && indexAge !== -1) {
      let i = 0;
      let gapYear;
      let gapAge;
      // Check if the successive years and ages are spaced the same
      do {
        i += 1;
        gapYear = primes[indexYear + i] - primes[indexYear];
        gapAge = primes[indexAge + i] - primes[indexAge];
      } while (gapAge === gapYear);
      // If the index is two or more, then we have consecutive prime matches
      // Print the results
      if (i >= 2) {
        total += i;
        sets += 1;
        if (!headingPrinted) {
          headingPrinted = true;
          console.log(`Born in ${yearOfBirth}`);
        }
        console.log(`   ${i} consecutive:`);
        for (let j = 0; j < i; j += 1) {
          console.log(`     ${primes[indexAge + j]} in ${primes[indexYear + j]}`);
        }
        // Skip over to the year of the last successful match
        age = primes[indexAge + (i - 1)];
      }
    }
    // Try out the next age
    age += 1;
  }
  if (total) {
    console.log(`  which makes ${sets} sets of primes for a total of ${total}`);
  }
}

Results

Born in 1896
   4 consecutive:
     97 in 1993
     101 in 1997
     103 in 1999
     107 in 2003
  which makes 1 sets of primes for a total of 4
Born in 1900
   2 consecutive:
     73 in 1973
     79 in 1979
  which makes 1 sets of primes for a total of 2
Born in 1902
   2 consecutive:
     29 in 1931
     31 in 1933
   2 consecutive:
     97 in 1999
     101 in 2003
  which makes 2 sets of primes for a total of 4
Born in 1904
   2 consecutive:
     83 in 1987
     89 in 1993
  which makes 1 sets of primes for a total of 2
Born in 1908
   2 consecutive:
     41 in 1949
     43 in 1951
  which makes 1 sets of primes for a total of 2
Born in 1912
   2 consecutive:
     61 in 1973
     67 in 1979
  which makes 1 sets of primes for a total of 2
Born in 1914
   2 consecutive:
     17 in 1931
     19 in 1933
   3 consecutive:
     73 in 1987
     79 in 1993
     83 in 1997
   2 consecutive:
     89 in 2003
     97 in 2011
  which makes 3 sets of primes for a total of 7
Born in 1920
   2 consecutive:
     11 in 1931
     13 in 1933
   2 consecutive:
     29 in 1949
     31 in 1951
   2 consecutive:
     53 in 1973
     59 in 1979
   2 consecutive:
     79 in 1999
     83 in 2003
   2 consecutive:
     107 in 2027
     109 in 2029
  which makes 5 sets of primes for a total of 10
Born in 1926
   2 consecutive:
     5 in 1931
     7 in 1933
   2 consecutive:
     47 in 1973
     53 in 1979
   4 consecutive:
     61 in 1987
     67 in 1993
     71 in 1997
     73 in 1999
   2 consecutive:
     101 in 2027
     103 in 2029
   2 consecutive:
     113 in 2039
     127 in 2053
  which makes 5 sets of primes for a total of 12
Born in 1928
   2 consecutive:
     3 in 1931
     5 in 1933
   2 consecutive:
     83 in 2011
     89 in 2017
  which makes 2 sets of primes for a total of 4
Born in 1932
   2 consecutive:
     17 in 1949
     19 in 1951
   2 consecutive:
     67 in 1999
     71 in 2003
  which makes 2 sets of primes for a total of 4
Born in 1934
   2 consecutive:
     53 in 1987
     59 in 1993
  which makes 1 sets of primes for a total of 2
Born in 1938
   2 consecutive:
     11 in 1949
     13 in 1951
   2 consecutive:
     59 in 1997
     61 in 1999
   2 consecutive:
     73 in 2011
     79 in 2017
  which makes 3 sets of primes for a total of 6
Born in 1940
   2 consecutive:
     47 in 1987
     53 in 1993
  which makes 1 sets of primes for a total of 2
Born in 1942
   2 consecutive:
     31 in 1973
     37 in 1979
  which makes 1 sets of primes for a total of 2
Born in 1944
   2 consecutive:
     5 in 1949
     7 in 1951
  which makes 1 sets of primes for a total of 2
Born in 1946
   2 consecutive:
     3 in 1949
     5 in 1951
  which makes 1 sets of primes for a total of 2
Born in 1950
   2 consecutive:
     23 in 1973
     29 in 1979
   2 consecutive:
     43 in 1993
     47 in 1997
   2 consecutive:
     61 in 2011
     67 in 2017
  which makes 3 sets of primes for a total of 6
Born in 1956
   5 consecutive:
     31 in 1987
     37 in 1993
     41 in 1997
     43 in 1999
     47 in 2003
   2 consecutive:
     71 in 2027
     73 in 2029
  which makes 2 sets of primes for a total of 7
Born in 1958
   2 consecutive:
     53 in 2011
     59 in 2017
  which makes 1 sets of primes for a total of 2
Born in 1962
   2 consecutive:
     37 in 1999
     41 in 2003
  which makes 1 sets of primes for a total of 2
Born in 1964
   2 consecutive:
     23 in 1987
     29 in 1993
   2 consecutive:
     47 in 2011
     53 in 2017
  which makes 2 sets of primes for a total of 4
Born in 1968
   2 consecutive:
     29 in 1997
     31 in 1999
   2 consecutive:
     59 in 2027
     61 in 2029
  which makes 2 sets of primes for a total of 4
Born in 1974
   2 consecutive:
     19 in 1993
     23 in 1997
   3 consecutive:
     107 in 2081
     109 in 2083
     113 in 2087
  which makes 2 sets of primes for a total of 5
Born in 1980
   4 consecutive:
     13 in 1993
     17 in 1997
     19 in 1999
     23 in 2003
   2 consecutive:
     31 in 2011
     37 in 2017
   2 consecutive:
     83 in 2063
     89 in 2069
   4 consecutive:
     101 in 2081
     103 in 2083
     107 in 2087
     109 in 2089
  which makes 4 sets of primes for a total of 12
Born in 1986
   4 consecutive:
     7 in 1993
     11 in 1997
     13 in 1999
     17 in 2003
   2 consecutive:
     41 in 2027
     43 in 2029
   3 consecutive:
     97 in 2083
     101 in 2087
     103 in 2089
  which makes 3 sets of primes for a total of 9
Born in 1988
   2 consecutive:
     23 in 2011
     29 in 2017
  which makes 1 sets of primes for a total of 2
Born in 1990
   2 consecutive:
     73 in 2063
     79 in 2069
  which makes 1 sets of primes for a total of 2
Born in 1992
   3 consecutive:
     5 in 1997
     7 in 1999
     11 in 2003
  which makes 1 sets of primes for a total of 3
Born in 1994
   2 consecutive:
     3 in 1997
     5 in 1999
  which makes 1 sets of primes for a total of 2
Born in 1998
   2 consecutive:
     29 in 2027
     31 in 2029
  which makes 1 sets of primes for a total of 2
Born in 2002
   2 consecutive:
     61 in 2063
     67 in 2069
  which makes 1 sets of primes for a total of 2
Born in 2004
   2 consecutive:
     79 in 2083
     83 in 2087
   2 consecutive:
     107 in 2111
     109 in 2113
  which makes 2 sets of primes for a total of 4
Born in 2010
   2 consecutive:
     17 in 2027
     19 in 2029
   2 consecutive:
     53 in 2063
     59 in 2069
   2 consecutive:
     71 in 2081
     73 in 2083
   2 consecutive:
     101 in 2111
     103 in 2113
  which makes 4 sets of primes for a total of 8
Born in 2016
   2 consecutive:
     11 in 2027
     13 in 2029
   2 consecutive:
     47 in 2063
     53 in 2069
   3 consecutive:
     67 in 2083
     71 in 2087
     73 in 2089
  which makes 3 sets of primes for a total of 7