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Block #266,140

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2013, 4:50:09 AM Β· Difficulty 9.9611 Β· 6,535,242 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
752c6b9ec875beaf315c878d5de92aaa15885bf9bd70a1d5f2adec296c754689
View on Chainz β†—

Height

#266,140

Difficulty

9.961083

Transactions

2

Size

391 B

Version

2

Bits

09f6098f

Nonce

15,085

Timestamp

11/20/2013, 4:50:09 AM

Confirmations

6,535,242

Mined by

⛏️ P2SHAJdBKrNM5AVKuZRfBVMVAtNzXCaWHH2pFc

Merkle Root

bdc5d7c4b28b8e7e378da4d0635dcc126c70998bd30a51a9b62267efd3f65d3a
Transactions (2)
Coinbase2b00031ba0c546…d6f207a176687a
1 in β†’ 1 out10.0700 XPM109 B
AJdBKrNM…aWHH2pFc
c77655bb61f868…053b98d8b0f92e
1 in β†’ 1 out3.9035 XPM193 B
AMNgsa3Q…TK8GA4dG
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.

1.296 Γ— 10⁹³(94-digit number)
12966528606738345514…92333584390672755039
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
1.296 Γ— 10⁹³(94-digit number)
12966528606738345514…92333584390672755039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.296 Γ— 10⁹³(94-digit number)
12966528606738345514…92333584390672755041
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
2.593 Γ— 10⁹³(94-digit number)
25933057213476691028…84667168781345510079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.593 Γ— 10⁹³(94-digit number)
25933057213476691028…84667168781345510081
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
5.186 Γ— 10⁹³(94-digit number)
51866114426953382057…69334337562691020159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.186 Γ— 10⁹³(94-digit number)
51866114426953382057…69334337562691020161
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
1.037 Γ— 10⁹⁴(95-digit number)
10373222885390676411…38668675125382040319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.037 Γ— 10⁹⁴(95-digit number)
10373222885390676411…38668675125382040321
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
2.074 Γ— 10⁹⁴(95-digit number)
20746445770781352822…77337350250764080639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.074 Γ— 10⁹⁴(95-digit number)
20746445770781352822…77337350250764080641
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:57,655,123 XPMΒ·at block #6,801,381 Β· updates every 60s
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