Block #2,491,166

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2018, 1:52:31 PM · Difficulty 10.9709 · 4,351,849 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

670f0860f40faa3fcdb9c41d3bde69c239f3f031c9d9a4143c5b0ae1bc098a40

View on Chainz ↗

Height

#2,491,166

Difficulty

10.970890

Transactions

Size

426 B

Version

Bits

0af88c3e

Nonce

1,281,271,529

Timestamp

1/26/2018, 1:52:31 PM

Confirmations

4,351,849

Mined by

⛏️ P2SHAdwjwuCNwDDSnZ89ZLVBF3c3uF36pgeenW

Merkle Root

315d1066e4ccb3843824077b1871c109f4d08d133bda17f907d2d4c8549b4094

Transactions (2)

Coinbase7443f46074d594…7abd1ffddba02c

1 in → 1 out8.3100 XPM109 B

AdwjwuCN…36pgeenW

61abd2f26cf3bf…1eeabf212f4899

1 in → 2 out153.8948 XPM227 B

ARcQq29x…kFCVGLt6 AdDSPtwE…P3JHB2wt

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.

3.007 × 10⁹⁵(96-digit number)

30078871542826012737…27859131729847019519

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

3.007 × 10⁹⁵(96-digit number)

30078871542826012737…27859131729847019519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.007 × 10⁹⁵(96-digit number)

30078871542826012737…27859131729847019521

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

6.015 × 10⁹⁵(96-digit number)

60157743085652025474…55718263459694039039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.015 × 10⁹⁵(96-digit number)

60157743085652025474…55718263459694039041

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

1.203 × 10⁹⁶(97-digit number)

12031548617130405094…11436526919388078079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.203 × 10⁹⁶(97-digit number)

12031548617130405094…11436526919388078081

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

2.406 × 10⁹⁶(97-digit number)

24063097234260810189…22873053838776156159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.406 × 10⁹⁶(97-digit number)

24063097234260810189…22873053838776156161

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

4.812 × 10⁹⁶(97-digit number)

48126194468521620379…45746107677552312319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.812 × 10⁹⁶(97-digit number)

48126194468521620379…45746107677552312321

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 #2,491,166

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