Problem 57810. List the two-bit primes

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 321px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.5px; transform-origin: 407px 160.5px; vertical-align: baseline; "><div style="block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.108px 8px; transform-origin: 313.108px 8px; unicode-bidi: normal; "><span style="">Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.8417px 8px; transform-origin: 52.8417px 8px; unicode-bidi: normal; "><span style="font-style: italic; ">New York Times.</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1083px 8px; transform-origin: 17.1083px 8px; unicode-bidi: normal; "><span style=""> This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.</span></span></div><div style="block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.058px 8px; transform-origin: 381.058px 8px; unicode-bidi: normal; "><span style="">In a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. </span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.875px 8px; transform-origin: 379.875px 8px; unicode-bidi: normal; "><span style="">Remember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.375px 8px; transform-origin: 80.375px 8px; unicode-bidi: normal; "><span style="">Write a function to list the </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; "><span style="">th two-bit and all its accompanying primes. </span></span></div></div></div>

Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the New York Times. This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.
In a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. 
Remember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. 
Write a function to list the th two-bit and all its accompanying primes.

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Problem 57810. List the two-bit primes

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