Block #265,739

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 8:40:58 PM · Difficulty 9.9618 · 6,541,843 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0f5e73f0a4c231877fc2a421d1c3c8d11835eebfc13765ac1a3d4225be8a54d

View on Chainz ↗

Height

#265,739

Difficulty

9.961751

Transactions

Size

1.91 KB

Version

Bits

09f63548

Nonce

119,635

Timestamp

11/19/2013, 8:40:58 PM

Confirmations

6,541,843

Mined by

⛏️ aRAMR89gp5bqXhfq7w5ebCAohteboZEXFX4Z

Merkle Root

8b58bb5fb9b2ca74900866ae1cdbe3b429cf8f9dce4dc9db8509544e7fa20836

Transactions (1)

Coinbase8b58bb5fb9b2ca…09544e7fa20836

1 in → 53 out10.0400 XPM1.82 KB

AMR89gp5…oZEXFX4Z AFqKfjez…qX9Ace3g APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs AP2GxFDi…MZQBdSYt

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.

1.589 × 10⁹⁶(97-digit number)

15895792275483182994…17628730846101053439

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

1.589 × 10⁹⁶(97-digit number)

15895792275483182994…17628730846101053439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.589 × 10⁹⁶(97-digit number)

15895792275483182994…17628730846101053441

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

3.179 × 10⁹⁶(97-digit number)

31791584550966365988…35257461692202106879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.179 × 10⁹⁶(97-digit number)

31791584550966365988…35257461692202106881

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

6.358 × 10⁹⁶(97-digit number)

63583169101932731976…70514923384404213759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.358 × 10⁹⁶(97-digit number)

63583169101932731976…70514923384404213761

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

1.271 × 10⁹⁷(98-digit number)

12716633820386546395…41029846768808427519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.271 × 10⁹⁷(98-digit number)

12716633820386546395…41029846768808427521

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

2.543 × 10⁹⁷(98-digit number)

25433267640773092790…82059693537616855039

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 #265,739

Cookie Preferences