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Block #31,015

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 9:40:10 PM Β· Difficulty 7.9879 Β· 6,778,939 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
362581df7b888a65b3c8f24d9ce403ac0a934da60189906419e4024d566f82bf
View on Chainz β†—

Height

#31,015

Difficulty

7.987944

Transactions

1

Size

198 B

Version

2

Bits

07fce9e1

Nonce

71

Timestamp

7/13/2013, 9:40:10 PM

Confirmations

6,778,939

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

bd0705cd6a77234a69a10a1403928117e6113fa09b2b50ad96add7e8b23e7122
Transactions (1)
Coinbasebd0705cd6a7723…add7e8b23e7122
1 in β†’ 1 out15.6500 XPM108 B
AV3Mx3Aq…AKiwER2W
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.608 Γ— 10⁹⁴(95-digit number)
56087027577941257322…64730072136523593349
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.608 Γ— 10⁹⁴(95-digit number)
56087027577941257322…64730072136523593349
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.608 Γ— 10⁹⁴(95-digit number)
56087027577941257322…64730072136523593351
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.121 Γ— 10⁹⁡(96-digit number)
11217405515588251464…29460144273047186699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.121 Γ— 10⁹⁡(96-digit number)
11217405515588251464…29460144273047186701
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.243 Γ— 10⁹⁡(96-digit number)
22434811031176502928…58920288546094373399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.243 Γ— 10⁹⁡(96-digit number)
22434811031176502928…58920288546094373401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.486 Γ— 10⁹⁡(96-digit number)
44869622062353005857…17840577092188746799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.486 Γ— 10⁹⁡(96-digit number)
44869622062353005857…17840577092188746801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,723,713 XPMΒ·at block #6,809,953 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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