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Yes.
For purposes of the proof, we will consider these integers in their base two notation.
We can easily see that 0 can be written as the sum of exactly two prome numbers:

Likewise, we can see that 1 can be written as the sum of exactly two prome numbers:

Every even integer greater than 10 (base two) can be written as a combination of only 1's and 0's, and thus can be written as the sum of exactly two prome numbers.
Proof complete.
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While Aziraphale was at the antiques auction, browsing a small pile of old religious books, he met Dorothy Thatchson. Dorothy Thatchson was 72 years old, grandmother of 23, great-grandmother of 4, and both she and Aziraphale owned the same edition of a misprinted 1820 bible.
When they realized this, she told Aziraphale how *nice* it was to find a young man who was interested in his Bible, these days. Then she proceeded to tell him how glad she was all those nasty Jews and gays and modern tarts were going to burn in Hell forever after.
Aziraphale excused himself and attempted to look very busy at a table across the room. She followed him.
"…and when those buggerers get there, you mark me, Satan will show them what the business end of a pitchfor--"
"Well!" Aziraphale said, grabbing a snuff box at random and waving it in front of her to interrupt. "Would you look at this!"
Dorothy's half open mouth twisted. She pointed a finger. "That," she said, and then took a breath, starting again from a higher octave. "That's Blasphemy!"
Aziraphale considered the snuff box again. A likeness of Dore's Lucifer spread it's wings over the top. "Oh," Aziraphale said. "I suppose it is. Nice silverwork, though."
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Tim shivered and pulled his cape tighter around him. "Okay," he said after surveying the death trap for a few seconds. "If we can get through the wall of ice cream in our way, I can open the safe door." He looked meaningfully at Bart, until Bart stopped licking his lips at the mound of ice cream in front of them and actually noticed.
"Oh! Oh!" said Bart. "I know!"
"I mean," Tim said, carefully enough that his teeth didn't clatter. "If you have any suggestions. On how to re. Remove it."
"Say it!" said Bart. "Are you going to say it?"
"No."
"Yes! Say it!"
Tim sighed. "Fine," he said. "This l-looks like a job… for Impulse."
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Kara flipped to the last page of the scrapbook. A large newsprint copy of a flying, fire-breathing anaconda chased a smaller figure in Supergirl's colours. "And that," she said, grinning at Jimmy, "is how you father and I fell in love." Jimmy smiled back at her.
On the armchair across the coffee table, James Olsen Junior sniffed and crossed his legs. "Last week," he said, unimpressed, "you guys said you fell in love when some invading aliens trapped you in the negative phantom zone and you had to escape using nothing but thoughtwaves and an imaginary salamander."
"And the week before that," his sister added, "it was when the Supergirl Emergency Squad was brainwashed by Dr Psycho and Dad trapped them in a special camera Mom made." Ally Olsen pulled the scrapbook closer to her, considering the photo thoughtfully. Jimmy had always said it was one of his best, and although Ally maintained that she was going to become a world famous chemist*, she had inherited his eye for photography.
"And this morning," said Jimmy, "when your mother was absentmindedly mixing the pancake dough too fast and it cooked before it hit the stove. Sometimes that's just how it goes." Kara turned to him and he kissed her lightly.
Ally and James rolled their eyes and groaned. But before they could make sarcastic comments, Streaky the Supercat landed on top of the scrapbook with news of a radioactive sea monster threatening the city, and Kara, James and Ally had to fly off to save the day.
* "Like Lex Luthor!" she had announced, after Luthor had given a particularly inspiring speech to her 9th grade class. It turned out that Luthor was wearing a tie that hypnotized his audience into believing everything that he said, but even after the effects wore off and Kara had returned the money the students stole from the bank, Ally sulked until her parents got her a chemistry set. And, when she blew that one up, another one.
It was somewhat worrying.
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Also, Kara/Jimmy= adorable.
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And thanks! I'm traditionally afeared of smoopy, so glad it worked out. :D
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And the super-family is super-cute. (but you've got an extra i in the cut text)
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Awww, Impulse! I like pained Robin.
You'd be pained too, if you were facing the prospect of an Impulse on *that much sugar*!
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Aziraphale! *squeaks*
Oh god, Impulse + wall of sugar-loaded ice cream = disaster ahead.
Kara and Jimmy are adorable.
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Hey, I didn't waste all these years in learning for *nothing*. ;)
Glad you liked these!
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