Block #54,793

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 10:14:33 PM · Difficulty 8.9366 · 6,754,805 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76162f350d1ff9465a2dc98bea5efa510d217c7b583dad0fc8158bbf085f0626

View on Chainz ↗

Height

#54,793

Difficulty

8.936591

Transactions

Size

202 B

Version

Bits

08efc474

Nonce

192

Timestamp

7/16/2013, 10:14:33 PM

Confirmations

6,754,805

Mined by

⛏️ P2SHAQEbmWMhm3AfNhyeGW1Fbr2Y8UbVPpCt5X

Merkle Root

293cec2c53dffb092cc1943ee4e326a737df9d0aadf209c8d4d4a040ad02ad29

Transactions (1)

Coinbase293cec2c53dffb…d4a040ad02ad29

1 in → 1 out12.5000 XPM110 B

AQEbmWMh…bVPpCt5X

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.

1.295 × 10¹⁰⁰(101-digit number)

12950663786675805254…24231526337480844289

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

1.295 × 10¹⁰⁰(101-digit number)

12950663786675805254…24231526337480844289

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.295 × 10¹⁰⁰(101-digit number)

12950663786675805254…24231526337480844291

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

2.590 × 10¹⁰⁰(101-digit number)

25901327573351610508…48463052674961688579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.590 × 10¹⁰⁰(101-digit number)

25901327573351610508…48463052674961688581

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

5.180 × 10¹⁰⁰(101-digit number)

51802655146703221016…96926105349923377159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.180 × 10¹⁰⁰(101-digit number)

51802655146703221016…96926105349923377161

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

1.036 × 10¹⁰¹(102-digit number)

10360531029340644203…93852210699846754319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10¹⁰¹(102-digit number)

10360531029340644203…93852210699846754321

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 #54,793

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