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Block #45,391

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 2:38:32 AM Β· Difficulty 8.7557 Β· 6,751,434 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
214354354ed3135b23c8e7171734e98c0ff3994c5136f333039329daa7494665
View on Chainz β†—

Height

#45,391

Difficulty

8.755676

Transactions

1

Size

200 B

Version

2

Bits

08c173f7

Nonce

28

Timestamp

7/15/2013, 2:38:32 AM

Confirmations

6,751,434

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

9747a4b55673efb46fa5b955bf7948f830c6113ccb63de942ea9b3e89436f874
Transactions (1)
Coinbase9747a4b55673ef…a9b3e89436f874
1 in β†’ 1 out13.0300 XPM110 B
AeTcmmqH…LrFchfe1
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.

3.544 Γ— 10⁹⁴(95-digit number)
35441512819094793918…85221614156724965899
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
3.544 Γ— 10⁹⁴(95-digit number)
35441512819094793918…85221614156724965899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.544 Γ— 10⁹⁴(95-digit number)
35441512819094793918…85221614156724965901
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
7.088 Γ— 10⁹⁴(95-digit number)
70883025638189587836…70443228313449931799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.088 Γ— 10⁹⁴(95-digit number)
70883025638189587836…70443228313449931801
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
1.417 Γ— 10⁹⁡(96-digit number)
14176605127637917567…40886456626899863599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.417 Γ— 10⁹⁡(96-digit number)
14176605127637917567…40886456626899863601
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
2.835 Γ— 10⁹⁡(96-digit number)
28353210255275835134…81772913253799727199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.835 Γ— 10⁹⁡(96-digit number)
28353210255275835134…81772913253799727201
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:57,618,610 XPMΒ·at block #6,796,824 Β· updates every 60s
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