A050445 Each prime appears later in alphabetical order (in American English) than the one before.

2, 211, 223, 2003, 2027, 2203, 2221, 2000000000003, 2000000000203, 2000000002001, 2000000002003, 2000000002223, 2000000000000000000000000000000000041, 2000000000000000000000000000000000429, 2000000000000000000000000000000000653

Offset: 1

Author

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 23 1999

Keywords

• base
• fini
• full
• nonn
• word

Comments

From Michael S. Branicky, Aug 17 2022: (Start)

As in the companion sequence A050444, spaces, hypens and the word "and" are not included in the comparisons.

In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.

The highest term is a(38) = 2*10^63 + 2*10^36 + 2*10^12 + 2202 ("two vigintillion two undecillion two trillion two thousand two hundred ninety three"). See b-file and link to US English names of terms. (End)

Examples

			Prime 2 ("two") is followed in alphabetic order first by prime 211 ("two hundred eleven").
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..38
• Michael S. Branicky, US English names of terms
• Eric Weisstein's World of Mathematics, Large Number
• Wikipedia, Names of Large Numbers
• Wiktionary, one hundred one (US)
• Wiktionary, one hundred and one (UK)

Crossrefs

Cf. A050444, A180301.

Programs

Python

from sympy import isprime
from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "").replace(chr(32), "").replace("-", "")
def afind(limit, start=2):
    alst, last, t = [], start-1, start
    while t <= limit:
        target = n2w(last)
        while not isprime(t) or n2w(t) <= target:
            t += 1
            if t > limit: return alst
        last = t; alst.append(t)
    return alst
print(afind(3000)) # Michael S. Branicky, Aug 17 2022

Extensions

If you accept "vigintillion" as a name for 10^63 then there are more terms.

Offset changed, a(4) inserted and a(8) and beyond from Michael S. Branicky, Aug 17 2022