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Block #75,973

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 8:32:58 PM Β· Difficulty 9.0580 Β· 6,733,723 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
422eb580ef998374502832e1ce4bae0fba45967f9e4543e93dac14c0f4c463a5
View on Chainz β†—

Height

#75,973

Difficulty

9.057951

Transactions

1

Size

202 B

Version

2

Bits

090ed5dc

Nonce

532

Timestamp

7/21/2013, 8:32:58 PM

Confirmations

6,733,723

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

512bd20e091b85b25debe89c07b615a26b86610d45dcda972607b6c238d18e00
Transactions (1)
Coinbase512bd20e091b85…07b6c238d18e00
1 in β†’ 1 out12.1700 XPM110 B
AVQxbFsH…KG2vYXbz
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.

3.864 Γ— 10⁹⁸(99-digit number)
38640558132468616006…43642131561363205639
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
3.864 Γ— 10⁹⁸(99-digit number)
38640558132468616006…43642131561363205639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.864 Γ— 10⁹⁸(99-digit number)
38640558132468616006…43642131561363205641
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
7.728 Γ— 10⁹⁸(99-digit number)
77281116264937232013…87284263122726411279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.728 Γ— 10⁹⁸(99-digit number)
77281116264937232013…87284263122726411281
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
1.545 Γ— 10⁹⁹(100-digit number)
15456223252987446402…74568526245452822559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.545 Γ— 10⁹⁹(100-digit number)
15456223252987446402…74568526245452822561
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
3.091 Γ— 10⁹⁹(100-digit number)
30912446505974892805…49137052490905645119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.091 Γ— 10⁹⁹(100-digit number)
30912446505974892805…49137052490905645121
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
6.182 Γ— 10⁹⁹(100-digit number)
61824893011949785610…98274104981811290239
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:57,721,645 XPMΒ·at block #6,809,695 Β· updates every 60s
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