# 205

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## Number

$205$ (**two hundred and five**) is:

- $5 \times 41$

- The $4$th positive integer after $200$, $202$, $204$ that cannot be made into a prime number by changing just $1$ digit

- The $10$th positive integer after $50$, $65$, $85$, $125$, $130$, $145$, $170$, $185$, $200$ which can be expressed as the sum of two square numbers in two or more different ways:
- $205 = 14^2 + 3^2 = 13^2 + 6^2$

- The $13$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$, $190$ the decimal representation of whose square can be split into two parts which are each themselves square:
- $205^2 = 42 \, 025$; $4 = 2^2$, $2025 = 45^2$

- The $40$th lucky number:
- $1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $163$, $169$, $171$, $189$, $193$, $195$, $201$, $205$, $\ldots$

- The number of pairs of twin primes less than $10 \, 000$

## Also see

*Previous ... Next*: Number of Twin Primes less than Powers of 10*Previous ... Next*: Squares whose Digits can be Separated into 2 other Squares*Previous ... Next*: Sum of 2 Squares in 2 Distinct Ways*Previous ... Next*: Lucky Number*Previous ... Next*: Numbers that cannot be made Prime by changing 1 Digit

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $205$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $205$