1709 (number)

• 267th prime number .
• When you include the prime number 1709 of the number 57 in the recording center, the result, 175709, is a prime number. When you include two numbers 57 in a row in the recording center of the number 1709, the result obtained, 17575709, is also a prime number. The result of continuing this process, with one more number 57 added each time, will be a sequence of 8 primes in a row (1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 - primes, but 175757575757575757653 = 234,467) ^1] .
• The number 1709 is one of the values ​​of degree q, using which you can get Wagstaff primes (primes of the form${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">p</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">=</span></span>\frac{{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">2</span></span>}}^{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">q</span></span>}}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">+</span></span>\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">one</span></span>}}{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">3</span></span>}}}$ {\ displaystyle p = {{2 ^ {q} +1} \ over 3}}   , where q is a prime number) ^[2] .

NGC 1709 (aka NGC 1717 ) is a lenticular galaxy in the constellation Orion .

Year of the Battle of Poltava, see also 1709 .