Block #54,492

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 8:45:37 PM · Difficulty 8.9339 · 6,736,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f2a1071b8b1b117b82fd16e49abe28e8189b23729e8e2c71f93d15016c7eb21

View on Chainz ↗

Height

#54,492

Difficulty

8.933854

Transactions

Size

200 B

Version

Bits

08ef1107

Nonce

Timestamp

7/16/2013, 8:45:37 PM

Confirmations

6,736,512

Merkle Root

982f16ed4c5df931e90846369e38c5ef883e9e563345c2e993187c2b7d4f161d

Transactions (1)

Coinbase982f16ed4c5df9…187c2b7d4f161d

1 in → 1 out12.5100 XPM110 B

AeTcmmqH…LrFchfe1

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.

5.020 × 10⁹⁵(96-digit number)

50205710062635354557…69139169791762813239

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

5.020 × 10⁹⁵(96-digit number)

50205710062635354557…69139169791762813239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.020 × 10⁹⁵(96-digit number)

50205710062635354557…69139169791762813241

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

1.004 × 10⁹⁶(97-digit number)

10041142012527070911…38278339583525626479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.004 × 10⁹⁶(97-digit number)

10041142012527070911…38278339583525626481

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

2.008 × 10⁹⁶(97-digit number)

20082284025054141822…76556679167051252959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.008 × 10⁹⁶(97-digit number)

20082284025054141822…76556679167051252961

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

4.016 × 10⁹⁶(97-digit number)

40164568050108283645…53113358334102505919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.016 × 10⁹⁶(97-digit number)

40164568050108283645…53113358334102505921

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

8.032 × 10⁹⁶(97-digit number)

80329136100216567291…06226716668205011839

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