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Block #2,813,692

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 10:54:18 AM Β· Difficulty 11.6791 Β· 4,027,414 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a669e557d21d807a90639c9c7e00572a4d08ac86007f70bce65ffa686b64a64a
View on Chainz β†—

Height

#2,813,692

Difficulty

11.679109

Transactions

1

Size

199 B

Version

2

Bits

0badda1c

Nonce

1,088,396,471

Timestamp

8/28/2018, 10:54:18 AM

Confirmations

4,027,414

Mined by

⛏️ P2SHAbAQ8SuFbbjt2ZbEPeKbBuxdVuhtgwLjq9

Merkle Root

64fd28aec0138d23a66363b18914b294451302344b9e646fedd0342f7bca34c1
Transactions (1)
Coinbase64fd28aec0138d…d0342f7bca34c1
1 in β†’ 1 out7.3200 XPM110 B
AbAQ8SuF…htgwLjq9
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.

1.405 Γ— 10⁹³(94-digit number)
14056848125671906870…73661203092753365929
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
1.405 Γ— 10⁹³(94-digit number)
14056848125671906870…73661203092753365929
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.405 Γ— 10⁹³(94-digit number)
14056848125671906870…73661203092753365931
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
2.811 Γ— 10⁹³(94-digit number)
28113696251343813741…47322406185506731859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.811 Γ— 10⁹³(94-digit number)
28113696251343813741…47322406185506731861
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
5.622 Γ— 10⁹³(94-digit number)
56227392502687627482…94644812371013463719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.622 Γ— 10⁹³(94-digit number)
56227392502687627482…94644812371013463721
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
1.124 Γ— 10⁹⁴(95-digit number)
11245478500537525496…89289624742026927439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.124 Γ— 10⁹⁴(95-digit number)
11245478500537525496…89289624742026927441
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
2.249 Γ— 10⁹⁴(95-digit number)
22490957001075050993…78579249484053854879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.249 Γ— 10⁹⁴(95-digit number)
22490957001075050993…78579249484053854881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.498 Γ— 10⁹⁴(95-digit number)
44981914002150101986…57158498968107709759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,973,213 XPMΒ·at block #6,841,105 Β· updates every 60s
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