Block #54,081

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 6:35:31 PM · Difficulty 8.9301 · 6,735,976 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

444cab9afac5bef0b8e23b93b7773219d04c1e9ae133b31d67f9d3a4009d0b01

View on Chainz ↗

Height

#54,081

Difficulty

8.930058

Transactions

Size

576 B

Version

Bits

08ee184f

Nonce

346

Timestamp

7/16/2013, 6:35:31 PM

Confirmations

6,735,976

Merkle Root

88d68c975b409eb62f75a3befedf271076a3a76398683ec39a584404642804ab

Transactions (2)

Coinbasebed110685791eb…3fe67ba0c7ca18

1 in → 1 out12.5300 XPM110 B

ANYiFhhz…dMe2kKYW

f1e946595e5826…f0c4d335aac287

2 in → 2 out987.7919 XPM374 B

AVG9rnE6…NKXxpBbN AQ5hWn2F…FcuMvSjP

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.

5.207 × 10⁹⁹(100-digit number)

52072436711189786169…32885098278737509639

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

5.207 × 10⁹⁹(100-digit number)

52072436711189786169…32885098278737509639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.207 × 10⁹⁹(100-digit number)

52072436711189786169…32885098278737509641

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

1.041 × 10¹⁰⁰(101-digit number)

10414487342237957233…65770196557475019279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.041 × 10¹⁰⁰(101-digit number)

10414487342237957233…65770196557475019281

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

2.082 × 10¹⁰⁰(101-digit number)

20828974684475914467…31540393114950038559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.082 × 10¹⁰⁰(101-digit number)

20828974684475914467…31540393114950038561

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

4.165 × 10¹⁰⁰(101-digit number)

41657949368951828935…63080786229900077119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.165 × 10¹⁰⁰(101-digit number)

41657949368951828935…63080786229900077121

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

8.331 × 10¹⁰⁰(101-digit number)

83315898737903657871…26161572459800154239

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