Block #2,468,646

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2018, 11:24:09 PM · Difficulty 10.9601 · 4,374,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a3b256b233cbf3f54dde4151cc1690214d63bd80c2e41f57a9d7aede5f3ee36

View on Chainz ↗

Height

#2,468,646

Difficulty

10.960084

Transactions

Size

571 B

Version

Bits

0af5c813

Nonce

1,591,967,789

Timestamp

1/11/2018, 11:24:09 PM

Confirmations

4,374,745

Mined by

⛏️ P2SHAUbXCxN3aUJY2FtVQKYGaigh5tDutUhpCX

Merkle Root

7cba7cf0892a6c7d5da7b4c105280541384f87c84f61f64d0c4df2532c70f3b4

Transactions (2)

Coinbase4a83fe904766b6…a055a74f538c12

1 in → 1 out8.3200 XPM109 B

AUbXCxN3…DutUhpCX

c772f11f3d946d…d77c0ebf6a530f

2 in → 2 out1001.0004 XPM372 B

AJvKjLrt…dfxfFtt3 AGpunVLw…oiaPy6rc

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.

2.326 × 10⁹⁴(95-digit number)

23262387638188653603…87939604738904780159

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

2.326 × 10⁹⁴(95-digit number)

23262387638188653603…87939604738904780159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.326 × 10⁹⁴(95-digit number)

23262387638188653603…87939604738904780161

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

4.652 × 10⁹⁴(95-digit number)

46524775276377307207…75879209477809560319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.652 × 10⁹⁴(95-digit number)

46524775276377307207…75879209477809560321

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

9.304 × 10⁹⁴(95-digit number)

93049550552754614414…51758418955619120639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.304 × 10⁹⁴(95-digit number)

93049550552754614414…51758418955619120641

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

1.860 × 10⁹⁵(96-digit number)

18609910110550922882…03516837911238241279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.860 × 10⁹⁵(96-digit number)

18609910110550922882…03516837911238241281

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

3.721 × 10⁹⁵(96-digit number)

37219820221101845765…07033675822476482559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.721 × 10⁹⁵(96-digit number)

37219820221101845765…07033675822476482561

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 #2,468,646

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