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Block #2,668,868

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2018, 8:36:14 PM Β· Difficulty 11.6768 Β· 4,172,995 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d5cea8cd041dc5d693fc9cb9012fa92f17bdd447c67ea2b3053b716008b83db
View on Chainz β†—

Height

#2,668,868

Difficulty

11.676807

Transactions

1

Size

200 B

Version

2

Bits

0bad4337

Nonce

1,879,176,873

Timestamp

5/19/2018, 8:36:14 PM

Confirmations

4,172,995

Mined by

⛏️ P2SHAGxyVX6XNS2JbyNWATS8kCFMGTQBL5WvkJ

Merkle Root

73f9224e03edc0df18c70c34c35480d04764d295b233cdfdfe8906cfdb4dcc62
Transactions (1)
Coinbase73f9224e03edc0…8906cfdb4dcc62
1 in β†’ 1 out7.3200 XPM110 B
AGxyVX6X…QBL5WvkJ
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.

6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771359
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
6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771361
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
1.348 Γ— 10⁹⁡(96-digit number)
13487858673505473191…14243413440279542719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.348 Γ— 10⁹⁡(96-digit number)
13487858673505473191…14243413440279542721
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
2.697 Γ— 10⁹⁡(96-digit number)
26975717347010946383…28486826880559085439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.697 Γ— 10⁹⁡(96-digit number)
26975717347010946383…28486826880559085441
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
5.395 Γ— 10⁹⁡(96-digit number)
53951434694021892767…56973653761118170879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.395 Γ— 10⁹⁡(96-digit number)
53951434694021892767…56973653761118170881
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
1.079 Γ— 10⁹⁢(97-digit number)
10790286938804378553…13947307522236341759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.079 Γ— 10⁹⁢(97-digit number)
10790286938804378553…13947307522236341761
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
2.158 Γ— 10⁹⁢(97-digit number)
21580573877608757107…27894615044472683519
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:57,979,282 XPMΒ·at block #6,841,862 Β· updates every 60s
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