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Block #373,276

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/24/2014, 5:02:21 AM Β· Difficulty 10.4253 Β· 6,453,434 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8b1cca6753d63f318d65ed1e6836aa94843db6c4c377a102e8be94199cd9b06f
View on Chainz β†—

Height

#373,276

Difficulty

10.425258

Transactions

1

Size

200 B

Version

2

Bits

0a6cddb5

Nonce

265,175

Timestamp

1/24/2014, 5:02:21 AM

Confirmations

6,453,434

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

910b1dca72e7d3385650d224066a4a3cbe887a48165562f8f3dce5af0546ff16
Transactions (1)
Coinbase910b1dca72e7d3…dce5af0546ff16
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.357 Γ— 10⁹⁡(96-digit number)
13572352853875336619…25093408224187391999
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
1.357 Γ— 10⁹⁡(96-digit number)
13572352853875336619…25093408224187391999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.357 Γ— 10⁹⁡(96-digit number)
13572352853875336619…25093408224187392001
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
2.714 Γ— 10⁹⁡(96-digit number)
27144705707750673238…50186816448374783999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.714 Γ— 10⁹⁡(96-digit number)
27144705707750673238…50186816448374784001
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
5.428 Γ— 10⁹⁡(96-digit number)
54289411415501346477…00373632896749567999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.428 Γ— 10⁹⁡(96-digit number)
54289411415501346477…00373632896749568001
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
1.085 Γ— 10⁹⁢(97-digit number)
10857882283100269295…00747265793499135999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.085 Γ— 10⁹⁢(97-digit number)
10857882283100269295…00747265793499136001
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
2.171 Γ— 10⁹⁢(97-digit number)
21715764566200538591…01494531586998271999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.171 Γ— 10⁹⁢(97-digit number)
21715764566200538591…01494531586998272001
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:57,857,832 XPMΒ·at block #6,826,709 Β· updates every 60s
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