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Block #73,629

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 6:57:30 AM Β· Difficulty 8.9950 Β· 6,740,436 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b74cabf9da8747c7e091733d6e528561753e44f2a9b42e663650779468cb82f
View on Chainz β†—

Height

#73,629

Difficulty

8.994954

Transactions

1

Size

200 B

Version

2

Bits

08feb54e

Nonce

211

Timestamp

7/21/2013, 6:57:30 AM

Confirmations

6,740,436

Mined by

⛏️ P2SHAHGPtSCNuYeecmqUQuK4cLJv6iGESamBFW

Merkle Root

48e4cc9f09c42231a843d32a5f2dc6027ea5f0f35ffa1e2aa306d8e72c5e1814
Transactions (1)
Coinbase48e4cc9f09c422…06d8e72c5e1814
1 in β†’ 1 out12.3400 XPM109 B
AHGPtSCN…GESamBFW
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.

1.575 Γ— 10⁹⁢(97-digit number)
15751484152975102383…23375458416529909579
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
1.575 Γ— 10⁹⁢(97-digit number)
15751484152975102383…23375458416529909579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.575 Γ— 10⁹⁢(97-digit number)
15751484152975102383…23375458416529909581
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
3.150 Γ— 10⁹⁢(97-digit number)
31502968305950204766…46750916833059819159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.150 Γ— 10⁹⁢(97-digit number)
31502968305950204766…46750916833059819161
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
6.300 Γ— 10⁹⁢(97-digit number)
63005936611900409532…93501833666119638319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.300 Γ— 10⁹⁢(97-digit number)
63005936611900409532…93501833666119638321
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
1.260 Γ— 10⁹⁷(98-digit number)
12601187322380081906…87003667332239276639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.260 Γ— 10⁹⁷(98-digit number)
12601187322380081906…87003667332239276641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁷(98-digit number)
25202374644760163812…74007334664478553279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,756,598 XPMΒ·at block #6,814,064 Β· updates every 60s
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