Block #79,526

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 1:10:25 PM · Difficulty 9.2458 · 6,714,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecd235bbfc2a7882feb3c3661ccba9db34a53995a3259d09c7e29692cabd2279

View on Chainz ↗

Height

#79,526

Difficulty

9.245798

Transactions

Size

427 B

Version

Bits

093eec99

Nonce

701

Timestamp

7/23/2013, 1:10:25 PM

Confirmations

6,714,660

Merkle Root

cc84b94f99a97026a941375c6809da9500ab8cf399e9cf61a8c1f7d4df66b200

Transactions (2)

Coinbasebe6508eee9e9a6…57ed9b3eda324a

1 in → 1 out11.6900 XPM110 B

AMqu1WaN…iNXaPcrK

59990b61151a24…130972e04227d6

1 in → 2 out50.6988 XPM227 B

AbjwRZwV…M7QSMJsD AKKb38vw…nN1DKpfW

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.

4.351 × 10⁹⁴(95-digit number)

43510088018070488350…42868340916560894739

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

4.351 × 10⁹⁴(95-digit number)

43510088018070488350…42868340916560894739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.351 × 10⁹⁴(95-digit number)

43510088018070488350…42868340916560894741

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

8.702 × 10⁹⁴(95-digit number)

87020176036140976700…85736681833121789479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.702 × 10⁹⁴(95-digit number)

87020176036140976700…85736681833121789481

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

1.740 × 10⁹⁵(96-digit number)

17404035207228195340…71473363666243578959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.740 × 10⁹⁵(96-digit number)

17404035207228195340…71473363666243578961

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

3.480 × 10⁹⁵(96-digit number)

34808070414456390680…42946727332487157919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.480 × 10⁹⁵(96-digit number)

34808070414456390680…42946727332487157921

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

6.961 × 10⁹⁵(96-digit number)

69616140828912781360…85893454664974315839

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