150 (number)

• 150 is the sum of eight consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31). Given 150, the Mertens function returns 0.^[1]
• 150 is conjectured to be the only minimal difference greater than 1 of any increasing arithmetic progression of n primes (in this case, n = 7) that is not a primorial (a product of the first m primes).^[2]
• The sum of Euler's totient function φ(x) over the first twenty-two integers is 150.
• 150 is a Harshad number and an abundant number.
• 150 degrees is the measure of the internal angle of a regular dodecagon.
• ${\displaystyle F_{11}(150)=150^{2048}+1}$ is the largest known generalized Fermat prime with even base less than 1000.^[3]

150 is also:

• The number of degrees in the quincunx astrological aspect explored by Johannes Kepler.
• The approximate value for Dunbar's number, a theoretical value with implications in sociology and anthropology. It is actually 148.