Block #76,776

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 4:02:51 AM · Difficulty 9.1222 · 6,732,964 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7554a8d87ea8872438beb4806b95d2fc3eb7d1f554816db94347318fa5d13f6

View on Chainz ↗

Height

#76,776

Difficulty

9.122171

Transactions

Size

206 B

Version

Bits

091f46a0

Nonce

463

Timestamp

7/22/2013, 4:02:51 AM

Confirmations

6,732,964

Mined by

⛏️ P2SHAMJGTwKci9EcXYd1pxeLH8kwwRk18kkTir

Merkle Root

1539ae30179b4d1524e469b6461a5d0e3a5c569c7e07e579aebfe2048d95b253

Transactions (1)

Coinbase1539ae30179b4d…bfe2048d95b253

1 in → 1 out12.0000 XPM110 B

AMJGTwKc…k18kkTir

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.

1.560 × 10¹⁰⁹(110-digit number)

15607563059153817663…03548462450856633519

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

1.560 × 10¹⁰⁹(110-digit number)

15607563059153817663…03548462450856633519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.560 × 10¹⁰⁹(110-digit number)

15607563059153817663…03548462450856633521

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

3.121 × 10¹⁰⁹(110-digit number)

31215126118307635326…07096924901713267039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.121 × 10¹⁰⁹(110-digit number)

31215126118307635326…07096924901713267041

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

6.243 × 10¹⁰⁹(110-digit number)

62430252236615270653…14193849803426534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.243 × 10¹⁰⁹(110-digit number)

62430252236615270653…14193849803426534081

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

1.248 × 10¹¹⁰(111-digit number)

12486050447323054130…28387699606853068159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.248 × 10¹¹⁰(111-digit number)

12486050447323054130…28387699606853068161

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

2.497 × 10¹¹⁰(111-digit number)

24972100894646108261…56775399213706136319

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 #76,776

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