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Block #3,144,042

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/18/2019, 12:15:44 AM Β· Difficulty 11.3221 Β· 3,696,007 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b04fc2d88870025ebabfef72deca6066fc23110fdff84efc18430501b7a9e5c0
View on Chainz β†—

Height

#3,144,042

Difficulty

11.322142

Transactions

1

Size

200 B

Version

2

Bits

0b5277ec

Nonce

777,344,038

Timestamp

4/18/2019, 12:15:44 AM

Confirmations

3,696,007

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

db3b18393ef8c693e3974f265825a5a2c574d8445780ed4e1b0583f15398906d
Transactions (1)
Coinbasedb3b18393ef8c6…0583f15398906d
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

5.020 Γ— 10⁹⁴(95-digit number)
50201274604954547204…56189022867674297919
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
5.020 Γ— 10⁹⁴(95-digit number)
50201274604954547204…56189022867674297919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.020 Γ— 10⁹⁴(95-digit number)
50201274604954547204…56189022867674297921
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
1.004 Γ— 10⁹⁡(96-digit number)
10040254920990909440…12378045735348595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.004 Γ— 10⁹⁡(96-digit number)
10040254920990909440…12378045735348595841
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
2.008 Γ— 10⁹⁡(96-digit number)
20080509841981818881…24756091470697191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.008 Γ— 10⁹⁡(96-digit number)
20080509841981818881…24756091470697191681
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
4.016 Γ— 10⁹⁡(96-digit number)
40161019683963637763…49512182941394383359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.016 Γ— 10⁹⁡(96-digit number)
40161019683963637763…49512182941394383361
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
8.032 Γ— 10⁹⁡(96-digit number)
80322039367927275526…99024365882788766719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.032 Γ— 10⁹⁡(96-digit number)
80322039367927275526…99024365882788766721
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
1.606 Γ— 10⁹⁢(97-digit number)
16064407873585455105…98048731765577533439
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
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