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Block #91,380

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2013, 9:42:15 PM Β· Difficulty 9.2194 Β· 6,704,612 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2585e12c9afeb16c901b6532d94c9d09e8608ff46f4d920848a7647b7a75cea9
View on Chainz β†—

Height

#91,380

Difficulty

9.219406

Transactions

1

Size

207 B

Version

2

Bits

09382b00

Nonce

200,209

Timestamp

7/31/2013, 9:42:15 PM

Confirmations

6,704,612

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

f9037f2d80c92bb93aefea850c3b13ebbef05add2940798fc6913391238ff1bb
Transactions (1)
Coinbasef9037f2d80c92b…913391238ff1bb
1 in β†’ 1 out11.7500 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.007 Γ— 10¹⁰⁷(108-digit number)
10072206293846570980…47635319138794459199
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
1.007 Γ— 10¹⁰⁷(108-digit number)
10072206293846570980…47635319138794459199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.007 Γ— 10¹⁰⁷(108-digit number)
10072206293846570980…47635319138794459201
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
2.014 Γ— 10¹⁰⁷(108-digit number)
20144412587693141960…95270638277588918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.014 Γ— 10¹⁰⁷(108-digit number)
20144412587693141960…95270638277588918401
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
4.028 Γ— 10¹⁰⁷(108-digit number)
40288825175386283920…90541276555177836799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.028 Γ— 10¹⁰⁷(108-digit number)
40288825175386283920…90541276555177836801
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
8.057 Γ— 10¹⁰⁷(108-digit number)
80577650350772567841…81082553110355673599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.057 Γ— 10¹⁰⁷(108-digit number)
80577650350772567841…81082553110355673601
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
1.611 Γ— 10¹⁰⁸(109-digit number)
16115530070154513568…62165106220711347199
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:57,612,024 XPMΒ·at block #6,795,991 Β· updates every 60s
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