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Block #286,153

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 6:57:24 PM Β· Difficulty 9.9852 Β· 6,512,915 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e91992ce10ab8f8d3fb91a7f8cadea350a3523d2826072b122097a954e6821ff
View on Chainz β†—

Height

#286,153

Difficulty

9.985219

Transactions

1

Size

200 B

Version

2

Bits

09fc3758

Nonce

23,458

Timestamp

11/30/2013, 6:57:24 PM

Confirmations

6,512,915

Mined by

⛏️ P2SHAczziGoaec4RPgvrGcUwYWvRLHdsHNtnSo

Merkle Root

71c786540939ac54689772a82d38d4d07439ebe2cf293b59f1cd39383a921177
Transactions (1)
Coinbase71c786540939ac…cd39383a921177
1 in β†’ 1 out10.0100 XPM109 B
AczziGoa…dsHNtnSo
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.

5.507 Γ— 10⁹⁢(97-digit number)
55079140938244216729…06409027376449951999
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
5.507 Γ— 10⁹⁢(97-digit number)
55079140938244216729…06409027376449951999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.507 Γ— 10⁹⁢(97-digit number)
55079140938244216729…06409027376449952001
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
1.101 Γ— 10⁹⁷(98-digit number)
11015828187648843345…12818054752899903999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.101 Γ— 10⁹⁷(98-digit number)
11015828187648843345…12818054752899904001
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
2.203 Γ— 10⁹⁷(98-digit number)
22031656375297686691…25636109505799807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.203 Γ— 10⁹⁷(98-digit number)
22031656375297686691…25636109505799808001
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
4.406 Γ— 10⁹⁷(98-digit number)
44063312750595373383…51272219011599615999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.406 Γ— 10⁹⁷(98-digit number)
44063312750595373383…51272219011599616001
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
8.812 Γ— 10⁹⁷(98-digit number)
88126625501190746767…02544438023199231999
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:57,636,586 XPMΒ·at block #6,799,067 Β· updates every 60s
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