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Block #76,233

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 10:46:03 PM Β· Difficulty 9.0814 Β· 6,719,921 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9e4d905ae9ec5ea44b1a8c0d789930d6e2f8700218243b59084082b76d69edd4
View on Chainz β†—

Height

#76,233

Difficulty

9.081438

Transactions

1

Size

201 B

Version

2

Bits

0914d91e

Nonce

63

Timestamp

7/21/2013, 10:46:03 PM

Confirmations

6,719,921

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

7bd33c30f42f6685650c2b1dcb59a8e49e9a605332cd2cd6b097d7041d85ac9b
Transactions (1)
Coinbase7bd33c30f42f66…97d7041d85ac9b
1 in β†’ 1 out12.1100 XPM110 B
AGCUbq6M…QSxWg1oL
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.

1.354 Γ— 10⁹⁸(99-digit number)
13547818107531041537…53752776240451425959
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
1.354 Γ— 10⁹⁸(99-digit number)
13547818107531041537…53752776240451425959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.354 Γ— 10⁹⁸(99-digit number)
13547818107531041537…53752776240451425961
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
2.709 Γ— 10⁹⁸(99-digit number)
27095636215062083074…07505552480902851919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.709 Γ— 10⁹⁸(99-digit number)
27095636215062083074…07505552480902851921
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
5.419 Γ— 10⁹⁸(99-digit number)
54191272430124166149…15011104961805703839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.419 Γ— 10⁹⁸(99-digit number)
54191272430124166149…15011104961805703841
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
1.083 Γ— 10⁹⁹(100-digit number)
10838254486024833229…30022209923611407679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10⁹⁹(100-digit number)
10838254486024833229…30022209923611407681
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
2.167 Γ— 10⁹⁹(100-digit number)
21676508972049666459…60044419847222815359
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:57,613,227 XPMΒ·at block #6,796,153 Β· updates every 60s
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