Block #718,544

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2014, 8:17:13 AM · Difficulty 10.9493 · 6,087,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

639ac5cc933499c5d6d51ceb86588d411fed1e086283bedc3d4675a96f077094

View on Chainz ↗

Height

#718,544

Difficulty

10.949337

Transactions

Size

27.68 KB

Version

Bits

0af307c6

Nonce

180,618,844

Timestamp

9/13/2014, 8:17:13 AM

Confirmations

6,087,248

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

58ab712a6fe31b81ae95ea2404b1dd16be0e950fcaf465ac9adbb09135f00215

Transactions (3)

Coinbase796e7c154b2954…300987bfa4d274

1 in → 1 out8.6200 XPM116 B

ANSXnLY2…Sd25TjkD

adafb47172120a…20ddb9c82c579f

183 in → 2 out59.3697 XPM26.53 KB

ANeJVWzu…V3xUF63z AS2bhQmo…2JCbfWN2

59bd770fcebb43…7797fa4df88f38

6 in → 2 out5.0163 XPM967 B

AM7BfPnY…wT9bGDpr AVSJEsci…H5gX1o8s

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.

3.324 × 10⁹⁷(98-digit number)

33244320296395474026…30163063185200814079

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

3.324 × 10⁹⁷(98-digit number)

33244320296395474026…30163063185200814079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.324 × 10⁹⁷(98-digit number)

33244320296395474026…30163063185200814081

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

6.648 × 10⁹⁷(98-digit number)

66488640592790948052…60326126370401628159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.648 × 10⁹⁷(98-digit number)

66488640592790948052…60326126370401628161

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

1.329 × 10⁹⁸(99-digit number)

13297728118558189610…20652252740803256319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.329 × 10⁹⁸(99-digit number)

13297728118558189610…20652252740803256321

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

2.659 × 10⁹⁸(99-digit number)

26595456237116379221…41304505481606512639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.659 × 10⁹⁸(99-digit number)

26595456237116379221…41304505481606512641

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

5.319 × 10⁹⁸(99-digit number)

53190912474232758442…82609010963213025279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.319 × 10⁹⁸(99-digit number)

53190912474232758442…82609010963213025281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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