Block #14,156

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 3:42:09 PM · Difficulty 7.8175 · 6,780,130 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef8e4c2d592aa4e0f0fe96f9fafe4af0b2ca9e7bf96141f942b2cdfadb77ae60

View on Chainz ↗

Height

#14,156

Difficulty

7.817508

Transactions

Size

1.26 KB

Version

Bits

07d1483c

Nonce

Timestamp

7/11/2013, 3:42:09 PM

Confirmations

6,780,130

Merkle Root

5b4272e70040cf3920fa3af59a6bd1dae45ff22645fa31d66069c2f09058c487

Transactions (2)

Coinbase5bd2e251ea0b33…ff7c84b3c9e40c

1 in → 1 out16.3600 XPM108 B

AMD88WR9…ZhWoLU4a

cd5a7011c4db73…7f3030085ca816

8 in → 2 out199.3800 XPM1.07 KB

AGRjaZ7X…BELEqeBa AYxoT5K3…VLfpXK9w

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.

3.318 × 10⁹⁶(97-digit number)

33185352360947362140…86640810836215202899

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

3.318 × 10⁹⁶(97-digit number)

33185352360947362140…86640810836215202899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.318 × 10⁹⁶(97-digit number)

33185352360947362140…86640810836215202901

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

6.637 × 10⁹⁶(97-digit number)

66370704721894724280…73281621672430405799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.637 × 10⁹⁶(97-digit number)

66370704721894724280…73281621672430405801

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

1.327 × 10⁹⁷(98-digit number)

13274140944378944856…46563243344860811599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.327 × 10⁹⁷(98-digit number)

13274140944378944856…46563243344860811601

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

2.654 × 10⁹⁷(98-digit number)

26548281888757889712…93126486689721623199

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