Block #118,081

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/15/2013, 12:48:23 PM · Difficulty 9.7506 · 6,690,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51e626b3553c7eeb9141e2cf253893d518c7b47dbb6b5e815c114d3b9382f4a1

View on Chainz ↗

Height

#118,081

Difficulty

9.750596

Transactions

Size

1.04 KB

Version

Bits

09c0270b

Nonce

416,150

Timestamp

8/15/2013, 12:48:23 PM

Confirmations

6,690,057

Mined by

⛏️ P2SHAPAj8ve7G418ePK9TGAGqxfrQNe9vPBLXR

Merkle Root

4d00a9a4aae4bf1a17e7762318ef56f859bf88e65d039a1683de46f218a77c7c

Transactions (3)

Coinbase83dc7910807e7f…ce916ba87646f6

1 in → 1 out10.5200 XPM109 B

APAj8ve7…e9vPBLXR

827a2c2a8af1ae…70574b00dfe17d

2 in → 1 out129.5600 XPM341 B

ATDg1wpK…dc5kwZ3e

19f6a83cd93752…8a32d4af4d6603

3 in → 2 out62.7983 XPM525 B

AV9Qt47E…jPEeqCB6 AK8vuDVg…WznaHSgU

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.

4.063 × 10⁹⁹(100-digit number)

40633809418091519269…17680659805274526369

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

4.063 × 10⁹⁹(100-digit number)

40633809418091519269…17680659805274526369

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.063 × 10⁹⁹(100-digit number)

40633809418091519269…17680659805274526371

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

8.126 × 10⁹⁹(100-digit number)

81267618836183038539…35361319610549052739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.126 × 10⁹⁹(100-digit number)

81267618836183038539…35361319610549052741

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

1.625 × 10¹⁰⁰(101-digit number)

16253523767236607707…70722639221098105479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.625 × 10¹⁰⁰(101-digit number)

16253523767236607707…70722639221098105481

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

3.250 × 10¹⁰⁰(101-digit number)

32507047534473215415…41445278442196210959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.250 × 10¹⁰⁰(101-digit number)

32507047534473215415…41445278442196210961

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

6.501 × 10¹⁰⁰(101-digit number)

65014095068946430831…82890556884392421919

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 #118,081

Cookie Preferences