Block #77,375

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 9:42:46 AM · Difficulty 9.1662 · 6,712,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f1497710597b1320eaf935bf59d21b85737f126b6eb39d074c201beb0225be4

View on Chainz ↗

Height

#77,375

Difficulty

9.166157

Transactions

Size

201 B

Version

Bits

092a8946

Nonce

167

Timestamp

7/22/2013, 9:42:46 AM

Confirmations

6,712,561

Merkle Root

3c76ee01ae3115297602f4c6bf40c02911eb0bff2b71fe9e49158c1de096e3d7

Transactions (1)

Coinbase3c76ee01ae3115…158c1de096e3d7

1 in → 1 out11.8900 XPM109 B

AK1JUKWL…oPR4rN5o

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.

1.824 × 10⁹⁹(100-digit number)

18245971112645559897…79872200775536841519

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

1.824 × 10⁹⁹(100-digit number)

18245971112645559897…79872200775536841519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.824 × 10⁹⁹(100-digit number)

18245971112645559897…79872200775536841521

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

3.649 × 10⁹⁹(100-digit number)

36491942225291119795…59744401551073683039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.649 × 10⁹⁹(100-digit number)

36491942225291119795…59744401551073683041

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

7.298 × 10⁹⁹(100-digit number)

72983884450582239591…19488803102147366079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.298 × 10⁹⁹(100-digit number)

72983884450582239591…19488803102147366081

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

1.459 × 10¹⁰⁰(101-digit number)

14596776890116447918…38977606204294732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.459 × 10¹⁰⁰(101-digit number)

14596776890116447918…38977606204294732161

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

2.919 × 10¹⁰⁰(101-digit number)

29193553780232895836…77955212408589464319

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