Simple check of Buenos Aires Constant (aka prime generating constant)

buenos_aires.py

import math
import sys

BAC = 2.920050977316134

def primes_BAC():
	item = BAC
	while True:
		next_prime = int(math.floor(item))
		yield next_prime
		item = next_prime * (item - next_prime + 1)

def primes():
	yield 2
	current = 3
	primes = [2]
	while True:
		i = 0
		prime = True
		while primes[i] * primes[i] <= current:
			if current % primes[i] == 0:
				prime = False
				break
			i += 1

		if prime:
			primes.append(current)
			yield current

		current += 1

for idx, (prime_bac, prime_simple) in enumerate(zip(primes_BAC(), primes())):
	if prime_bac != prime_simple:
		print(f"Failed at {idx}: generated {prime_bac}, but correct is {prime_simple}")
		break
	if idx % 1000 == 999:
		print(f"Everything good up to {idx}")

buenos_aires_decimal.py

import math
import sys
from decimal import *
decimal_places = int(sys.argv[1])

getcontext().prec = decimal_places

BAC = Decimal('2.920050977316134712092562917112019468002727899321426719772682533107733772127766124190178112317583742298338859553101376655790789350859005320458879066450802184292252411229314474766432726781359401611930934817871151893525264603575379521810813046420167707977389570250111803809282686178658154888032203367829269125018738690914047486202261291216227368389829929455587891569755355387051873925153818160795717143424044663393262377616866023439422418496621696030394939023411977293803544096857594931022126398510871655055416847798060973123630164611574876105859201981461135440151697900932470462567084428160424925578714793121712974479882318073408039208192925733361718397515791447897048836410034817769998489023206039246045593238665161843153486393205335710706553090212523695784940062438701975579958564876909551757478171387837461948559472493761934243132609402333680301736898869114665897851582285975980667789889845956308635891790746893363179701184088676786462101030418130966192439808238720725713956534268643753471734394623')

def primes_BAC():
	item = BAC
	while True:
		next_prime = math.floor(item)
		yield int(next_prime)
		item = next_prime * (item - next_prime + 1)

def primes():
	yield 2
	current = 3
	primes = [2]
	while True:
		i = 0
		prime = True
		while primes[i] * primes[i] <= current:
			if current % primes[i] == 0:
				prime = False
				break
			i += 1

		if prime:
			primes.append(current)
			yield current

		current += 1

for idx, (prime_bac, prime_simple) in enumerate(zip(primes_BAC(), primes())):
	if prime_bac != prime_simple:
		print(f"{decimal_places} decimal places failed at {idx}: generated {prime_bac}, but correct is {prime_simple}")
		break
	if idx % 1000 == 999:
		print(f"Everything good up to {idx}")

buenos_aires_gen.py

import math
import sys
from decimal import *

n = int(sys.argv[1])

def sieve(n):
	prime = [True for i in range(n+1)]
	prime[0] = False
	prime[1] = False
	p = 2
	while (p * p <= n):
		if (prime[p] == True):
			for i in range(p * p, n+1, p):
				prime[i] = False
		p += 1

	return [idx for idx, p in enumerate(prime) if p]

primes = sieve(n)
getcontext().prec = n
b = Decimal(0)
pp = Decimal(1)
for p in primes:
	b += Decimal(p - 1) / pp
	pp *= p

print(b)