# When is 2 About the Same as 70 Million?

A “twin prime” is a pair of prime numbers that differ by two. For example, 11 and 13, or 857 and 859. The “twin prime conjecture” states that there are an infinite number of twin primes. To this day, nobody has ever been able to prove this. It’s one of the great open conjectures of number theory.

Recently, however, an unknown mathematician proved a theorem that, according to the experts, is almost the same thing. It turns out that there are an infinite number of prime pairs that differ by some number N. And what is N? We still don’t know, but Yitang Zhang of the University of New Hampshire has demonstrated that it’s less than 70 million.

This is why I love number theory. I mean, what’s a difference of 69,999,998 between friends? Also this:

Without communicating with the field’s experts, Zhang started thinking about the problem. After three years, however, he had made no progress. “I was so tired,” he said. To take a break, Zhang visited a friend in Colorado last summer. There, on July 3, during a half-hour lull in his friend’s backyard before leaving for a concert, the solution suddenly came to him. “I immediately realized that it would work,” he said.

Isn’t that just perfect?

### WHO DOESN’T LOVE A POSITIVE STORY—OR TWO?

“Great journalism really does make a difference in this world: it can even save kids.”

That’s what a civil rights lawyer wrote to Julia Lurie, the day after her major investigation into a psychiatric hospital chain that uses foster children as “cash cows” published, letting her know he was using her findings that same day in a hearing to keep a child out of one of the facilities we investigated.

That’s awesome. As is the fact that Julia, who spent a full year reporting this challenging story, promptly heard from a Senate committee that will use her work in their own investigation of Universal Health Services. There’s no doubt her revelations will continue to have a big impact in the months and years to come.

Like another story about Mother Jones’ real-world impact.

This one, a multiyear investigation, published in 2021, exposed conditions in sugar work camps in the Dominican Republic owned by Central Romana—the conglomerate behind brands like C&H and Domino, whose product ends up in our Hershey bars and other sweets. A year ago, the Biden administration banned sugar imports from Central Romana. And just recently, we learned of a previously undisclosed investigation from the Department of Homeland Security, looking into working conditions at Central Romana. How big of a deal is this?

“This could be the first time a corporation would be held criminally liable for forced labor in their own supply chains,” according to a retired special agent we talked to.

Wow.

And it is only because Mother Jones is funded primarily by donations from readers that we can mount ambitious, yearlong—or more—investigations like these two stories that are making waves.

About that: It’s unfathomably hard in the news business right now, and we came up about \$28,000 short during our recent fall fundraising campaign. We simply have to make that up soon to avoid falling further behind than can be made up for, or needing to somehow trim \$1 million from our budget, like happened last year.

If you can, please support the reporting you get from Mother Jones—that exists to make a difference, not a profit—with a donation of any amount today. We need more donations than normal to come in from this specific blurb to help close our funding gap before it gets any bigger.

### WHO DOESN’T LOVE A POSITIVE STORY—OR TWO?

“Great journalism really does make a difference in this world: it can even save kids.”

That’s what a civil rights lawyer wrote to Julia Lurie, the day after her major investigation into a psychiatric hospital chain that uses foster children as “cash cows” published, letting her know he was using her findings that same day in a hearing to keep a child out of one of the facilities we investigated.

That’s awesome. As is the fact that Julia, who spent a full year reporting this challenging story, promptly heard from a Senate committee that will use her work in their own investigation of Universal Health Services. There’s no doubt her revelations will continue to have a big impact in the months and years to come.

Like another story about Mother Jones’ real-world impact.

This one, a multiyear investigation, published in 2021, exposed conditions in sugar work camps in the Dominican Republic owned by Central Romana—the conglomerate behind brands like C&H and Domino, whose product ends up in our Hershey bars and other sweets. A year ago, the Biden administration banned sugar imports from Central Romana. And just recently, we learned of a previously undisclosed investigation from the Department of Homeland Security, looking into working conditions at Central Romana. How big of a deal is this?

“This could be the first time a corporation would be held criminally liable for forced labor in their own supply chains,” according to a retired special agent we talked to.

Wow.

And it is only because Mother Jones is funded primarily by donations from readers that we can mount ambitious, yearlong—or more—investigations like these two stories that are making waves.

About that: It’s unfathomably hard in the news business right now, and we came up about \$28,000 short during our recent fall fundraising campaign. We simply have to make that up soon to avoid falling further behind than can be made up for, or needing to somehow trim \$1 million from our budget, like happened last year.

If you can, please support the reporting you get from Mother Jones—that exists to make a difference, not a profit—with a donation of any amount today. We need more donations than normal to come in from this specific blurb to help close our funding gap before it gets any bigger.