Block #266,093

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 3:55:17 AM · Difficulty 9.9611 · 6,543,862 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fae6109a182729a7eac48a1198d1e2e98c97d818e0698cf48a5bc0f1478f4649

View on Chainz ↗

Height

#266,093

Difficulty

9.961135

Transactions

Size

3.59 KB

Version

Bits

09f60cef

Nonce

61,655

Timestamp

11/20/2013, 3:55:17 AM

Confirmations

6,543,862

Mined by

⛏️ maR2AU9KdB9rpz9LAxy9pEhEHibVcuo5XC6WMy

Merkle Root

876357a3a9b37b956b77b8bc830f6f05f8600f133d7ec8e1aa3700c0963da69e

Transactions (2)

Coinbase6d08343ce06c49…e51a93df538328

1 in → 51 out10.0400 XPM1.75 KB

AU9KdB9r…o5XC6WMy AdnG9gQ7…N9B7mA2p APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs ALSiuDiS…WqQxGQSY

d4e1ede5881142…b830a46d4b92ad

12 in → 1 out11.4100 XPM1.74 KB

Ac3z4Ekf…7e3munF3

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.

4.366 × 10⁹⁴(95-digit number)

43664199721351942578…63708158099580380159

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

4.366 × 10⁹⁴(95-digit number)

43664199721351942578…63708158099580380159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.366 × 10⁹⁴(95-digit number)

43664199721351942578…63708158099580380161

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

8.732 × 10⁹⁴(95-digit number)

87328399442703885156…27416316199160760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.732 × 10⁹⁴(95-digit number)

87328399442703885156…27416316199160760321

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

1.746 × 10⁹⁵(96-digit number)

17465679888540777031…54832632398321520639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.746 × 10⁹⁵(96-digit number)

17465679888540777031…54832632398321520641

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

3.493 × 10⁹⁵(96-digit number)

34931359777081554062…09665264796643041279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.493 × 10⁹⁵(96-digit number)

34931359777081554062…09665264796643041281

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

6.986 × 10⁹⁵(96-digit number)

69862719554163108125…19330529593286082559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #266,093

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