Block #596,955

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2014, 12:55:14 PM · Difficulty 10.9338 · 6,209,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

428fc04776b89fd26a35beb1cf0fa7f31fa99cd5da44272c1eaedf754ab33394

View on Chainz ↗

Height

#596,955

Difficulty

10.933817

Transactions

Size

3.20 KB

Version

Bits

0aef0e9b

Nonce

48,286,707

Timestamp

6/21/2014, 12:55:14 PM

Confirmations

6,209,210

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9832f60eaa62188d12caac22d2913a8b3cdab883a4675863691fa6190e40d867

Transactions (2)

Coinbase68faea7f79b492…cdde5f761b90c9

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

3a246c8312df49…bc508178de13b5

23 in → 2 out104.8227 XPM3.00 KB

AMveus6J…HLqG4Sw4 AJVwetHH…7RSvsSkW

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.

3.316 × 10⁹⁸(99-digit number)

33163678294081328439…16501208637115215679

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

3.316 × 10⁹⁸(99-digit number)

33163678294081328439…16501208637115215679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.316 × 10⁹⁸(99-digit number)

33163678294081328439…16501208637115215681

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

6.632 × 10⁹⁸(99-digit number)

66327356588162656879…33002417274230431359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.632 × 10⁹⁸(99-digit number)

66327356588162656879…33002417274230431361

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

1.326 × 10⁹⁹(100-digit number)

13265471317632531375…66004834548460862719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.326 × 10⁹⁹(100-digit number)

13265471317632531375…66004834548460862721

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

2.653 × 10⁹⁹(100-digit number)

26530942635265062751…32009669096921725439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.653 × 10⁹⁹(100-digit number)

26530942635265062751…32009669096921725441

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

5.306 × 10⁹⁹(100-digit number)

53061885270530125503…64019338193843450879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.306 × 10⁹⁹(100-digit number)

53061885270530125503…64019338193843450881

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