Block #44,537

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 11:58:34 PM · Difficulty 8.7196 · 6,772,698 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78f94a1a40dd71559c1d333bb4d494bacff699a9b588fa0019a078a8bf1e2e2a

View on Chainz ↗

Height

#44,537

Difficulty

8.719601

Transactions

Size

695 B

Version

Bits

08b837cb

Nonce

Timestamp

7/14/2013, 11:58:34 PM

Confirmations

6,772,698

Mined by

⛏️ P2SHAZakk5h5eLU2tGV73YyAxzB4cAgiTZcejN

Merkle Root

9814262bff78894666e6e84c4c25c2bdb911558d3dd11a9248899db3936d7d20

Transactions (2)

Coinbasefb9e81f696a77e…fde83befceb8d1

1 in → 1 out13.1400 XPM109 B

AZakk5h5…giTZcejN

828dabf4274954…88d10427b9487f

3 in → 1 out632.0000 XPM489 B

AVESjiW6…UXTrjJNX

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.

9.896 × 10¹¹⁰(111-digit number)

98967111413413573426…41526584579442036319

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

9.896 × 10¹¹⁰(111-digit number)

98967111413413573426…41526584579442036319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.896 × 10¹¹⁰(111-digit number)

98967111413413573426…41526584579442036321

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

1.979 × 10¹¹¹(112-digit number)

19793422282682714685…83053169158884072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.979 × 10¹¹¹(112-digit number)

19793422282682714685…83053169158884072641

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

3.958 × 10¹¹¹(112-digit number)

39586844565365429370…66106338317768145279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.958 × 10¹¹¹(112-digit number)

39586844565365429370…66106338317768145281

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

7.917 × 10¹¹¹(112-digit number)

79173689130730858741…32212676635536290559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.917 × 10¹¹¹(112-digit number)

79173689130730858741…32212676635536290561

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 #44,537

Cookie Preferences