n := 12; p:=2; PRIME 2

NiM+SSJuRzYiIiM3NiM+SSJwRzYiIiIj

f := x-> (1-x)*cos(Pi*x) + (1/Pi)*sin(Pi*x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmIiIiRi85JCEiIkYvLUkkY29zR0YlNiMqJkkjUGlHSSpwcm90ZWN0ZWRHRjdGL0YwRi9GL0YvKiZGNkYxLUkkc2luR0YlRjRGL0YvRiVGJUYl

bnd := b->n*(gamma+log(8*Pi))-(n/2)*int((1-f(x/b))/sinh(x/2),x=0..b) -(n/2)*int(csch(x/2),x=b..infinity)-4*int(f(x/b)*cosh(x/2),x=0..b);

NiM+SSRibmRHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKiomSSJuR0YlIiIiLCZJJmdhbW1hR0kqcHJvdGVjdGVkR0YyRi8tSSRsb2dHRiU2IywkSSNQaUdGMiIiKUYvRi9GLyomRi5GLy1JJGludEdGJTYkKiYsJkYvRi8tSSJmR0YlNiMqJkkieEdGJUYvOSQhIiJGRUYvLUklc2luaEdGJTYjLCRGQyNGLyIiI0ZFL0ZDOyIiIUZERi8jRkVGSyomRi5GLy1GOzYkLUklY3NjaEdGJUZIL0ZDO0ZESSlpbmZpbml0eUdGMkYvRk8tRjs2JComRj9GLy1JJWNvc2hHRiVGSEYvRkwhIiVGJUYlRiU=

lcl := b->2*sum(log(p)*f(m*log(p)/b)*p^(-m/2),m=1..6);

NiM+SSRsY2xHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJC1JJHN1bUc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqKC1JJGxvZ0dGLzYjSSJwR0YlIiIiLUkiZkdGJTYjKihJIm1HRiVGOEY0Rjg5JCEiIkY4KUY3LCRGPSNGPyIiI0Y4L0Y9O0Y4IiInRkNGJUYlRiU=

num := 1; NUMBER OF PRIMES IN S

NiM+SSRudW1HNiIiIiI=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLyIqNHZlSio+JSEjOA==

evalf(bb/log(p)); CHECK UPPER LIMIT ON SUM IN LCL

NiMkIi8+OCk9SyRlZyEjOA==

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi9mWng0PjM7ISIj

num := 2;

NiM+SSRudW1HNiIiIiM=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL1RJPjQhPVMlISM4

evalf(bb/log(p));

NiMkIi8yRWRqWF1qISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi8iSCQqUkspKVIoISIj

num :=3;

NiM+SSRudW1HNiIiIiQ=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLzpoVkJGIWYlISM4

evalf(bb/log(p));

NiMkIi8jZWs5akJpJyEjOA==

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi9MZWRoRy9PISIi

n := 12; p:=3; PRIME 3

NiM+SSJuRzYiIiM3NiM+SSJwRzYiIiIk

f := x-> (1-x)*cos(Pi*x) + (1/Pi)*sin(Pi*x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmIiIiRi85JCEiIkYvLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjVJKF9zeXNsaWJHRiU2IyomSSNQaUdGNUYvRjBGL0YvRi8qJkY5RjEtSSRzaW5HRjRGN0YvRi9GJUYlRiU=

lcl := b->2*sum(log(p)*f(m*log(p)/b)*p^(-m/2),m=1..3);

NiM+SSRsY2xHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJC1JJHN1bUc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqKC1JJGxvZ0dGLzYjSSJwR0YlIiIiLUkiZkdGJTYjKihJIm1HRiVGOEY0Rjg5JCEiIkY4KUY3LCRGPSNGPyIiI0Y4L0Y9O0Y4IiIkRkNGJUYlRiU=

num := 1; NUMBER OF PRIMES IN S

NiM+SSRudW1HNiIiIiI=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLzVHblFaKT4lISM4

evalf(bb/log(p));

NiMkIi9wJ2ZnOjsjUSEjOA==

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi94bz4nKnpVNiEiIw==

num := 2;

NiM+SSRudW1HNiIiIiM=

lcl := b->2*sum(log(p)*f(m*log(p)/b)*p^(-m/2),m=1..4);

NiM+SSRsY2xHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJC1JJHN1bUc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqKC1JJGxvZ0dGLzYjSSJwR0YlIiIiLUkiZkdGJTYjKihJIm1HRiVGOEY0Rjg5JCEiIkY4KUY3LCRGPSNGPyIiI0Y4L0Y9O0Y4IiIlRkNGJUYlRiU=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL25CZHFxKlIlISM4

evalf(bb/log(p));

NiMkIi9RO1xmeS9TISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi92IUcyY1V0JCEiIw==

num :=3;

NiM+SSRudW1HNiIiIiQ=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLzY0K1VXJ2UlISM4

evalf(bb/log(p));

NiMkIi8iZTtVaFo8JSEjOA==

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi9BaSwyLCJIIiEiIg==

n := 12; p:=5; PRIME 5

NiM+SSJuRzYiIiM3NiM+SSJwRzYiIiIm

f := x-> (1-x)*cos(Pi*x) + (1/Pi)*sin(Pi*x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmIiIiRi85JCEiIkYvLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjVJKF9zeXNsaWJHRiU2IyomSSNQaUdGNUYvRjBGL0YvRi8qJkY5RjEtSSRzaW5HRjRGN0YvRi9GJUYlRiU=

lcl := b->2*sum(log(p)*f(m*log(p)/b)*p^(-m/2),m=1..2);

NiM+SSRsY2xHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJC1JJHN1bUc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqKC1JJGxvZ0dGLzYjSSJwR0YlIiIiLUkiZkdGJTYjKihJIm1HRiVGOEY0Rjg5JCEiIkY4KUY3LCRGPSNGPyIiI0Y4L0Y9O0Y4RkNGQ0YlRiVGJQ==

num := 1; NUMBER OF PRIMES IN S

NiM+SSRudW1HNiIiIiI=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL107aFVVIz4lISM4

evalf(bb/log(p));

NiMkIi9yJlJsKipbZyMhIzg=

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi8wOXg6cil6KCEiJA==

num := 2;

NiM+SSRudW1HNiIiIiM=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL04iKSl5ZDxSJSEjOA==

evalf(bb/log(p));

NiMkIi9USlFEdkdGISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi86eChSZlJ0IiEiIw==

num :=3;

NiM+SSRudW1HNiIiIiQ=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLyEqKSoqKTNneFghIzg=

evalf(bb/log(p));

NiMkIi84VVxMQVdHISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi8iNEQoUUp0UyEiIw==

n := 12; p:=7; PRIME 7

NiM+SSJuRzYiIiM3NiM+SSJwRzYiIiIo

f := x-> (1-x)*cos(Pi*x) + (1/Pi)*sin(Pi*x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmIiIiRi85JCEiIkYvLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjVJKF9zeXNsaWJHRiU2IyomSSNQaUdGNUYvRjBGL0YvRi8qJkY5RjEtSSRzaW5HRjRGN0YvRi9GJUYlRiU=

lcl := b->2*sum(log(p)*f(m*log(p)/b)*p^(-m/2),m=1..2);

NiM+SSRsY2xHNiJmKjYjSSJiR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJC1JJHN1bUc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqKC1JJGxvZ0dGLzYjSSJwR0YlIiIiLUkiZkdGJTYjKihJIm1HRiVGOEY0Rjg5JCEiIkY4KUY3LCRGPSNGPyIiI0Y4L0Y9O0Y4RkNGQ0YlRiVGJQ==

num := 1; NUMBER OF PRIMES IN S

NiM+SSRudW1HNiIiIiI=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL2RMNy1jIT0lISM4

evalf(bb/log(p));

NiMkIi9pSGpIUVtAISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi9eQy1UPCFIJyEiJA==

num := 2;

NiM+SSRudW1HNiIiIiM=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL2VRMidRK1AlISM4

evalf(bb/log(p));

NiMkIi91VSdmYmRDIyEjOA==

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi9AZi5vcz82ISIj

num :=3;

NiM+SSRudW1HNiIiIiQ=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiL2NXdz0mM2IlISM4

evalf(bb/log(p));

NiMkIi9kbk5fblFCISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi95JCo0XlQqNCMhIiM=

num := 0; BOUND WITHOUT LOCAL CORRECTIONS

NiM+SSRudW1HNiIiIiE=

bb := fsolve(diff(bnd(b)+num*lcl(b),b)=0,b,0..8);

NiM+SSNiYkc2IiQiLyVwO1M7OSlSISM4

evalf(exp(bnd(bb)+num*lcl(bb)));

NiMkIi8kcDg8WnNzJCEiJA==