Block #51,220

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 4:48:44 AM · Difficulty 8.8952 · 6,744,919 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c2545e1bd99f14778afd879d8ce0634e598183ff19347555dda91d79315a019

View on Chainz ↗

Height

#51,220

Difficulty

8.895165

Transactions

Size

201 B

Version

Bits

08e52986

Nonce

Timestamp

7/16/2013, 4:48:44 AM

Confirmations

6,744,919

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

3e870a5bd610395f06daf666052a08940a7bddd08ba97dca03f9d71b173de42d

Transactions (1)

Coinbase3e870a5bd61039…f9d71b173de42d

1 in → 1 out12.6200 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.

1.113 × 10⁹⁶(97-digit number)

11132972949766769343…30610369550046023999

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

1.113 × 10⁹⁶(97-digit number)

11132972949766769343…30610369550046023999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.113 × 10⁹⁶(97-digit number)

11132972949766769343…30610369550046024001

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

2.226 × 10⁹⁶(97-digit number)

22265945899533538686…61220739100092047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.226 × 10⁹⁶(97-digit number)

22265945899533538686…61220739100092048001

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

4.453 × 10⁹⁶(97-digit number)

44531891799067077372…22441478200184095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.453 × 10⁹⁶(97-digit number)

44531891799067077372…22441478200184096001

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

8.906 × 10⁹⁶(97-digit number)

89063783598134154745…44882956400368191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.906 × 10⁹⁶(97-digit number)

89063783598134154745…44882956400368192001

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