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Block #371,022

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/22/2014, 1:49:43 PM Β· Difficulty 10.4358 Β· 6,436,949 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f08cf57dd4193871193e21699e42bb2298bf6221db211fd4ca8494e08e0be38d
View on Chainz β†—

Height

#371,022

Difficulty

10.435774

Transactions

1

Size

200 B

Version

2

Bits

0a6f8ede

Nonce

92,617

Timestamp

1/22/2014, 1:49:43 PM

Confirmations

6,436,949

Mined by

⛏️ P2SHAddPxoMXBQQyF3UwDFeHLzbttJLJ9QJdVK

Merkle Root

8a2186060c86a11018fcdfb0129258915ce7fc20066a808fdf259ee01161d5fe
Transactions (1)
Coinbase8a2186060c86a1…259ee01161d5fe
1 in β†’ 1 out9.1700 XPM109 B
AddPxoMX…LJ9QJdVK
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.

1.040 Γ— 10⁹⁸(99-digit number)
10407103518566589003…29501038322741551999
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
1.040 Γ— 10⁹⁸(99-digit number)
10407103518566589003…29501038322741551999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.040 Γ— 10⁹⁸(99-digit number)
10407103518566589003…29501038322741552001
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
2.081 Γ— 10⁹⁸(99-digit number)
20814207037133178007…59002076645483103999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.081 Γ— 10⁹⁸(99-digit number)
20814207037133178007…59002076645483104001
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
4.162 Γ— 10⁹⁸(99-digit number)
41628414074266356015…18004153290966207999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.162 Γ— 10⁹⁸(99-digit number)
41628414074266356015…18004153290966208001
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
8.325 Γ— 10⁹⁸(99-digit number)
83256828148532712031…36008306581932415999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.325 Γ— 10⁹⁸(99-digit number)
83256828148532712031…36008306581932416001
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
1.665 Γ— 10⁹⁹(100-digit number)
16651365629706542406…72016613163864831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.665 Γ— 10⁹⁹(100-digit number)
16651365629706542406…72016613163864832001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,707,812 XPMΒ·at block #6,807,970 Β· updates every 60s
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