Block #14,661

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 5:17:32 PM · Difficulty 7.8318 · 6,775,011 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49a75e4056c6a623933e0a96c203345fc94038546d633a585cb7f736980496e9

View on Chainz ↗

Height

#14,661

Difficulty

7.831757

Transactions

Size

198 B

Version

Bits

07d4ee0f

Nonce

270

Timestamp

7/11/2013, 5:17:32 PM

Confirmations

6,775,011

Merkle Root

368e38fd709b48e20cfc56bf26e50d19902c7bc032ec955e12c110371168f693

Transactions (1)

Coinbase368e38fd709b48…c110371168f693

1 in → 1 out16.2800 XPM108 B

Aen8PBRb…bhERMxXC

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.

1.363 × 10⁹⁵(96-digit number)

13637825950450282267…81638419975664744749

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

1.363 × 10⁹⁵(96-digit number)

13637825950450282267…81638419975664744749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.363 × 10⁹⁵(96-digit number)

13637825950450282267…81638419975664744751

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

2.727 × 10⁹⁵(96-digit number)

27275651900900564534…63276839951329489499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.727 × 10⁹⁵(96-digit number)

27275651900900564534…63276839951329489501

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

5.455 × 10⁹⁵(96-digit number)

54551303801801129069…26553679902658978999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.455 × 10⁹⁵(96-digit number)

54551303801801129069…26553679902658979001

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

1.091 × 10⁹⁶(97-digit number)

10910260760360225813…53107359805317957999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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