Those Fascinating Numbers 361

211 111 322 112

• the 33rd insolite number (see the number 111).

211 121 114 112

• the

34th

insolite number (see the number 111).

215 523 459 072 (=

216

·

33

·

3492)

• the 1 000 000th powerful number (see the number 3 136).

221 322 261 600

• the 16th powerful number n such that n+1 is also powerful: here 221 322 261 600 =

25 · 35 · 52 · 112 · 972 and 221 322 261 601 = 74 · 96012 (see the number 288).

232 250 619 601 (=7 · 11 · 13 · 17 · 31 · 37 · 73 · 163)

• the smallest Carmichael number which is the product of eight prime numbers

(see the number 41 041).

250 330 350 875 (=

53

·

112

·

194

· 127)

• (possibly) the only number whose index of composition is 2.2 and which can

be written as the sum of two co-prime numbers whose index of composition is

≥ 6: indeed,

250 330 350 875 =

53

·

112

·

194

· 127 =

311

·

74

+

223

·

313,

where

λ(53

·

112

·

194

· 127) ≈ 2.225,

λ(311

·

74)

≈ 6.52594,

λ(223

·

313)

≈ 6.35898;

four other numbers

1013

with an index of composition ≥ 2 can be written

as the sum of two numbers whose index of

composition207

is ≥ 6: these are

607 323 321, 398 656 076 841, 44 496 177 152 and 1 625 169 742 057.

252 096 675 073

• the 10 000 000 000th prime power, in fact here a prime number (see the number

419).

207One

can easily show that assuming the abc Conjecture, there can only be finitely many such

numbers.