Block #1,120,246

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2015, 2:53:05 AM · Difficulty 10.9343 · 5,690,909 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3597aae8c918bc4916fb3247a82382f8e57b4f405ed747cc0acd96f717982415

View on Chainz ↗

Height

#1,120,246

Difficulty

10.934349

Transactions

Size

1.14 KB

Version

Bits

0aef3182

Nonce

299,938,482

Timestamp

6/21/2015, 2:53:05 AM

Confirmations

5,690,909

Mined by

⛏️ P2SHAYCEFfEvA8bq3M8XdiaRTWiFy8VxFT6jiA

Merkle Root

37eaa9bedf5be0b941bed0f1e13d5e43d7d6abb13a190fcc309350378ec48313

Transactions (2)

Coinbased2ffb4088188c7…a11d0a93e6be8e

1 in → 1 out8.3900 XPM110 B

AYCEFfEv…VxFT6jiA

9f669344bc36a6…3a294a173e1e7a

6 in → 2 out7.4611 XPM967 B

AVYjNJEW…jTeas9v4 AHtNq6CL…iYDg6AaL

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.

1.001 × 10⁹⁷(98-digit number)

10011733800313971052…14735835768813752319

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

1.001 × 10⁹⁷(98-digit number)

10011733800313971052…14735835768813752319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.001 × 10⁹⁷(98-digit number)

10011733800313971052…14735835768813752321

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

2.002 × 10⁹⁷(98-digit number)

20023467600627942105…29471671537627504639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.002 × 10⁹⁷(98-digit number)

20023467600627942105…29471671537627504641

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

4.004 × 10⁹⁷(98-digit number)

40046935201255884210…58943343075255009279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.004 × 10⁹⁷(98-digit number)

40046935201255884210…58943343075255009281

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

8.009 × 10⁹⁷(98-digit number)

80093870402511768421…17886686150510018559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.009 × 10⁹⁷(98-digit number)

80093870402511768421…17886686150510018561

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

1.601 × 10⁹⁸(99-digit number)

16018774080502353684…35773372301020037119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.601 × 10⁹⁸(99-digit number)

16018774080502353684…35773372301020037121

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

Block #1,120,246

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