Block #726,978

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/18/2014, 6:50:47 AM · Difficulty 10.9612 · 6,067,749 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

977770628e9ebd691513c5cad5e102ee0214e5135ee1275703a9937b72018e96

View on Chainz ↗

Height

#726,978

Difficulty

10.961238

Transactions

Size

59.19 KB

Version

Bits

0af613b1

Nonce

114,759,496

Timestamp

9/18/2014, 6:50:47 AM

Confirmations

6,067,749

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6534fa74752d7d60663dc4a8394c5ab8c5b8f97dde1bcdd497a27f5bc13f4c4b

Transactions (3)

Coinbase11d708f96cf2ef…ef5b38cbe50a1e

1 in → 1 out8.9400 XPM116 B

ANSXnLY2…Sd25TjkD

e468f89fff793c…e4bcb00d12302a

406 in → 2 out300.0100 XPM58.77 KB

AKynpQaS…jZf6o7cX AXW9HfxP…pQzshn9m

aa098d0f27ecd3…47aafdfab0ff6b

1 in → 2 out6.2897 XPM224 B

AYrwBKyU…1S6w2wRP AcXispzC…chXMXUBz

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.

1.558 × 10⁹⁸(99-digit number)

15583842991650369432…17228142699156485119

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

1.558 × 10⁹⁸(99-digit number)

15583842991650369432…17228142699156485119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.558 × 10⁹⁸(99-digit number)

15583842991650369432…17228142699156485121

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

3.116 × 10⁹⁸(99-digit number)

31167685983300738864…34456285398312970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.116 × 10⁹⁸(99-digit number)

31167685983300738864…34456285398312970241

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

6.233 × 10⁹⁸(99-digit number)

62335371966601477729…68912570796625940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.233 × 10⁹⁸(99-digit number)

62335371966601477729…68912570796625940481

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

1.246 × 10⁹⁹(100-digit number)

12467074393320295545…37825141593251880959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12467074393320295545…37825141593251880961

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

2.493 × 10⁹⁹(100-digit number)

24934148786640591091…75650283186503761919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.493 × 10⁹⁹(100-digit number)

24934148786640591091…75650283186503761921

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