Block #41,475

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:42:35 PM · Difficulty 8.5277 · 6,750,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbcdddf92efa4cdbef83e5cab9cb7539e81cb0cd6302cc7c2825136157ec6875

View on Chainz ↗

Height

#41,475

Difficulty

8.527688

Transactions

Size

12.91 KB

Version

Bits

0887168f

Nonce

106

Timestamp

7/14/2013, 4:42:35 PM

Confirmations

6,750,439

Merkle Root

2b95fa7e9709c92c9a9da2a6d56aa095a8ddba8db593c1c0e7acd152e9821109

Transactions (3)

Coinbase25b719a43ef186…02172039afafcc

1 in → 1 out13.8700 XPM109 B

Abx7PyfA…ynn8Gk7M

45b9b567037cf2…f4bc9c215a9437

112 in → 1 out2000.0000 XPM12.56 KB

AVDE9j9c…DXexEzBD

dd64ce1777766a…2406b5fe082c9c

1 in → 1 out15.6200 XPM159 B

AaNMrVuB…vz8xMmHF

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.

4.041 × 10⁹⁶(97-digit number)

40410176238503703208…92945782284575398659

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

4.041 × 10⁹⁶(97-digit number)

40410176238503703208…92945782284575398659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.041 × 10⁹⁶(97-digit number)

40410176238503703208…92945782284575398661

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

8.082 × 10⁹⁶(97-digit number)

80820352477007406416…85891564569150797319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.082 × 10⁹⁶(97-digit number)

80820352477007406416…85891564569150797321

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

1.616 × 10⁹⁷(98-digit number)

16164070495401481283…71783129138301594639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.616 × 10⁹⁷(98-digit number)

16164070495401481283…71783129138301594641

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

3.232 × 10⁹⁷(98-digit number)

32328140990802962566…43566258276603189279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.232 × 10⁹⁷(98-digit number)

32328140990802962566…43566258276603189281

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