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Block #274,291

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2013, 5:41:55 AM Β· Difficulty 9.9570 Β· 6,562,122 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e251224f880091a64a577a4a631b384f17c6ce6258a98cd4edcbcddaf151d7f4
View on Chainz β†—

Height

#274,291

Difficulty

9.956981

Transactions

1

Size

201 B

Version

2

Bits

09f4fcb8

Nonce

109,881

Timestamp

11/26/2013, 5:41:55 AM

Confirmations

6,562,122

Mined by

⛏️ P2SHAGGH2QmXkqegP22oTbAHjGHTa2JvtQK5sm

Merkle Root

068bc6e2ee27091ac107f867dffbebff1d581a21805f68c674305a9ba4ea29be
Transactions (1)
Coinbase068bc6e2ee2709…305a9ba4ea29be
1 in β†’ 1 out10.0700 XPM109 B
AGGH2QmX…JvtQK5sm
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.

9.163 Γ— 10⁹⁹(100-digit number)
91639930090509268580…44510181179483081659
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
9.163 Γ— 10⁹⁹(100-digit number)
91639930090509268580…44510181179483081659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.163 Γ— 10⁹⁹(100-digit number)
91639930090509268580…44510181179483081661
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
1.832 Γ— 10¹⁰⁰(101-digit number)
18327986018101853716…89020362358966163319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.832 Γ— 10¹⁰⁰(101-digit number)
18327986018101853716…89020362358966163321
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
3.665 Γ— 10¹⁰⁰(101-digit number)
36655972036203707432…78040724717932326639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.665 Γ— 10¹⁰⁰(101-digit number)
36655972036203707432…78040724717932326641
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
7.331 Γ— 10¹⁰⁰(101-digit number)
73311944072407414864…56081449435864653279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.331 Γ— 10¹⁰⁰(101-digit number)
73311944072407414864…56081449435864653281
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
1.466 Γ— 10¹⁰¹(102-digit number)
14662388814481482972…12162898871729306559
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:57,935,569 XPMΒ·at block #6,836,412 Β· updates every 60s
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