Block #41,119

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:06:53 PM · Difficulty 8.4967 · 6,775,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

710a8f632b884dd327a8f12dbe953a716884c9e3ca4814b9c4ad810f66e35351

View on Chainz ↗

Height

#41,119

Difficulty

8.496707

Transactions

Size

689 B

Version

Bits

087f2833

Nonce

279

Timestamp

7/14/2013, 4:06:53 PM

Confirmations

6,775,716

Mined by

⛏️ P2SHAQUZLYwwoEBtnqoqk78rJksb5vW65MgAU5

Merkle Root

f392401294ee6c00302a76fcb7d5895b4445b943839f0ad8d5b5750f1bfc8a3b

Transactions (2)

Coinbasec2d3385df78d96…c8d218fe784179

1 in → 1 out13.8400 XPM110 B

AQUZLYww…W65MgAU5

550f831eca3197…09062b575fa0f1

3 in → 2 out28.4200 XPM487 B

AccN9Axq…tJCNZ8bv AFmxRaDi…JMATMzon

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.

2.026 × 10⁹⁸(99-digit number)

20265622067109764235…22178162083607094739

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

2.026 × 10⁹⁸(99-digit number)

20265622067109764235…22178162083607094739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.026 × 10⁹⁸(99-digit number)

20265622067109764235…22178162083607094741

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

4.053 × 10⁹⁸(99-digit number)

40531244134219528471…44356324167214189479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.053 × 10⁹⁸(99-digit number)

40531244134219528471…44356324167214189481

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

8.106 × 10⁹⁸(99-digit number)

81062488268439056943…88712648334428378959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.106 × 10⁹⁸(99-digit number)

81062488268439056943…88712648334428378961

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

1.621 × 10⁹⁹(100-digit number)

16212497653687811388…77425296668856757919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.621 × 10⁹⁹(100-digit number)

16212497653687811388…77425296668856757921

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #41,119

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