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Block #2,108,951

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/9/2017, 9:27:04 PM Β· Difficulty 10.8986 Β· 4,709,082 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5e8d52db642c50cfa31bfbdc62e0b3a5db754ffe264b55ddbcb6faa3e5170edb
View on Chainz β†—

Height

#2,108,951

Difficulty

10.898551

Transactions

2

Size

85.10 KB

Version

2

Bits

0ae60773

Nonce

1,859,534,526

Timestamp

5/9/2017, 9:27:04 PM

Confirmations

4,709,082

Mined by

⛏️ P2SHAWb82vJ2aGhm7D7n93Mje5C1n86Cimi68U

Merkle Root

807529b892267724a7ce6109fe20abd1491193ea97775184f84a754f731d84b9
Transactions (2)
Coinbase9959b4734813de…c1eead542dd703
1 in β†’ 1 out9.2800 XPM110 B
AWb82vJ2…6Cimi68U
aa0c8edd4586bd…96e1c835f5c9b4
587 in β†’ 2 out5.0095 XPM84.91 KB
AUjBeKZH…3MTP1SQkARqu8p83…2Ed9uXtP
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.

2.521 Γ— 10⁹⁢(97-digit number)
25217985814942675065…94667399280339230719
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
2.521 Γ— 10⁹⁢(97-digit number)
25217985814942675065…94667399280339230719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.521 Γ— 10⁹⁢(97-digit number)
25217985814942675065…94667399280339230721
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
5.043 Γ— 10⁹⁢(97-digit number)
50435971629885350131…89334798560678461439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.043 Γ— 10⁹⁢(97-digit number)
50435971629885350131…89334798560678461441
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
1.008 Γ— 10⁹⁷(98-digit number)
10087194325977070026…78669597121356922879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.008 Γ— 10⁹⁷(98-digit number)
10087194325977070026…78669597121356922881
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
2.017 Γ— 10⁹⁷(98-digit number)
20174388651954140052…57339194242713845759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.017 Γ— 10⁹⁷(98-digit number)
20174388651954140052…57339194242713845761
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
4.034 Γ— 10⁹⁷(98-digit number)
40348777303908280105…14678388485427691519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.034 Γ— 10⁹⁷(98-digit number)
40348777303908280105…14678388485427691521
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
8.069 Γ— 10⁹⁷(98-digit number)
80697554607816560210…29356776970855383039
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:57,788,333 XPMΒ·at block #6,818,032 Β· updates every 60s
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