Block #2,809,223

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/25/2018, 11:37:57 AM · Difficulty 11.6665 · 4,030,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

289dca120baf999bb9c2b3f4ab1db7ba8747246607e6ceeacd4d9a998fe3ac63

View on Chainz ↗

Height

#2,809,223

Difficulty

11.666526

Transactions

Size

574 B

Version

Bits

0baaa16f

Nonce

54,555,648

Timestamp

8/25/2018, 11:37:57 AM

Confirmations

4,030,448

Mined by

⛏️ P2SHAdPjJAEz3jmF3aPJGkeN6cL4APwBu86hQR

Merkle Root

a693f061710023f65fe6540d93432c1bdb151497e5d69840b94c455250e3963d

Transactions (2)

Coinbase77c22e28676605…91b54fd0efc30a

1 in → 1 out7.3400 XPM110 B

AdPjJAEz…wBu86hQR

1833546a51c029…548c5ff6a2faaf

2 in → 2 out6.0071 XPM374 B

ANtDsPHw…eoG2UsS3 AQzna5sB…toxGhGNZ

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.494 × 10⁹⁴(95-digit number)

24941880124463989245…82060495568290680319

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.494 × 10⁹⁴(95-digit number)

24941880124463989245…82060495568290680319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.494 × 10⁹⁴(95-digit number)

24941880124463989245…82060495568290680321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.988 × 10⁹⁴(95-digit number)

49883760248927978490…64120991136581360639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.988 × 10⁹⁴(95-digit number)

49883760248927978490…64120991136581360641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

9.976 × 10⁹⁴(95-digit number)

99767520497855956981…28241982273162721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.976 × 10⁹⁴(95-digit number)

99767520497855956981…28241982273162721281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.995 × 10⁹⁵(96-digit number)

19953504099571191396…56483964546325442559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.995 × 10⁹⁵(96-digit number)

19953504099571191396…56483964546325442561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.990 × 10⁹⁵(96-digit number)

39907008199142382792…12967929092650885119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.990 × 10⁹⁵(96-digit number)

39907008199142382792…12967929092650885121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.981 × 10⁹⁵(96-digit number)

79814016398284765585…25935858185301770239

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,809,223

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