Block #395,995

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 3:05:37 AM · Difficulty 10.4090 · 6,431,313 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef52a0f7ccde98f3ff354aa61679357dee369fef320617d0639920a6e2b8ed6c

View on Chainz ↗

Height

#395,995

Difficulty

10.408983

Transactions

Size

1.44 KB

Version

Bits

0a68b317

Nonce

30,304

Timestamp

2/9/2014, 3:05:37 AM

Confirmations

6,431,313

Mined by

⛏️ P2SHAPoDvrmCVSAUMshvJejUQLpChW6Pa8sor6

Merkle Root

1c9b8fa2875af44dd18d02824f677e88563865e076b92e1428ac7f6fe099a86d

Transactions (2)

Coinbaseabdedb06593331…dc1b659f494405

1 in → 1 out9.2400 XPM109 B

APoDvrmC…6Pa8sor6

5005aff765352c…8805b379b4df0c

6 in → 16 out51.5771 XPM1.24 KB

AcvuG43Q…sF2abTGT AQsbr9JG…MmSbqgZu AKWUoUXA…MDXHzRkm AXf6j4ZH…PR8MjaKk AVRSjnEd…SARf4wT4

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.

8.687 × 10⁹⁴(95-digit number)

86872473064487378884…61739421264922200639

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

8.687 × 10⁹⁴(95-digit number)

86872473064487378884…61739421264922200639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.687 × 10⁹⁴(95-digit number)

86872473064487378884…61739421264922200641

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

1.737 × 10⁹⁵(96-digit number)

17374494612897475776…23478842529844401279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.737 × 10⁹⁵(96-digit number)

17374494612897475776…23478842529844401281

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

3.474 × 10⁹⁵(96-digit number)

34748989225794951553…46957685059688802559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.474 × 10⁹⁵(96-digit number)

34748989225794951553…46957685059688802561

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

6.949 × 10⁹⁵(96-digit number)

69497978451589903107…93915370119377605119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.949 × 10⁹⁵(96-digit number)

69497978451589903107…93915370119377605121

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

1.389 × 10⁹⁶(97-digit number)

13899595690317980621…87830740238755210239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.389 × 10⁹⁶(97-digit number)

13899595690317980621…87830740238755210241

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 #395,995

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