Block #54,220

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 7:18:56 PM · Difficulty 8.9314 · 6,756,195 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02518dcf4390b3c288e83bbe5e4ee3850f8a7a0740d728faed2223457664f903

View on Chainz ↗

Height

#54,220

Difficulty

8.931368

Transactions

Size

204 B

Version

Bits

08ee6e29

Nonce

Timestamp

7/16/2013, 7:18:56 PM

Confirmations

6,756,195

Mined by

⛏️ P2SHAQEbmWMhm3AfNhyeGW1Fbr2Y8UbVPpCt5X

Merkle Root

32cc5cf3313836f32d82733bad0c7efbdb842452ea1ec19ed58d2f011bb373bb

Transactions (1)

Coinbase32cc5cf3313836…8d2f011bb373bb

1 in → 1 out12.5200 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.

4.843 × 10¹⁰³(104-digit number)

48432557248422251485…67707076540206348479

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

4.843 × 10¹⁰³(104-digit number)

48432557248422251485…67707076540206348479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.843 × 10¹⁰³(104-digit number)

48432557248422251485…67707076540206348481

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

9.686 × 10¹⁰³(104-digit number)

96865114496844502970…35414153080412696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.686 × 10¹⁰³(104-digit number)

96865114496844502970…35414153080412696961

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

1.937 × 10¹⁰⁴(105-digit number)

19373022899368900594…70828306160825393919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.937 × 10¹⁰⁴(105-digit number)

19373022899368900594…70828306160825393921

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

3.874 × 10¹⁰⁴(105-digit number)

38746045798737801188…41656612321650787839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.874 × 10¹⁰⁴(105-digit number)

38746045798737801188…41656612321650787841

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

7.749 × 10¹⁰⁴(105-digit number)

77492091597475602376…83313224643301575679

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 #54,220

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