Block #395,145

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 12:28:14 PM · Difficulty 10.4124 · 6,417,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ed63129a50944febbab92006af7dbec122d549565a2fd1ac20812f5cd2c63ff

View on Chainz ↗

Height

#395,145

Difficulty

10.412353

Transactions

Size

576 B

Version

Bits

0a698ff7

Nonce

16,557

Timestamp

2/8/2014, 12:28:14 PM

Confirmations

6,417,505

Mined by

⛏️ P2SHAKVPaLfp27Zsdr88sxFczu2PwBGJewQjh6

Merkle Root

19e332f5dc19668fa0e0c88b16912ee113484d6030fdbc40c5794d98b6cb50e0

Transactions (2)

Coinbasef4d94341d62d22…aaaf0e3dfa28de

1 in → 1 out9.2200 XPM109 B

AKVPaLfp…GJewQjh6

278e061808398c…428489fa920d54

2 in → 2 out200.0001 XPM375 B

AM3Uks4t…pWT7rfZV AcXWuNYg…S4wucSpL

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.

4.730 × 10¹⁰⁰(101-digit number)

47303775609060856761…63128884944215573319

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

4.730 × 10¹⁰⁰(101-digit number)

47303775609060856761…63128884944215573319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.730 × 10¹⁰⁰(101-digit number)

47303775609060856761…63128884944215573321

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

9.460 × 10¹⁰⁰(101-digit number)

94607551218121713522…26257769888431146639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.460 × 10¹⁰⁰(101-digit number)

94607551218121713522…26257769888431146641

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

1.892 × 10¹⁰¹(102-digit number)

18921510243624342704…52515539776862293279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.892 × 10¹⁰¹(102-digit number)

18921510243624342704…52515539776862293281

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

3.784 × 10¹⁰¹(102-digit number)

37843020487248685409…05031079553724586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.784 × 10¹⁰¹(102-digit number)

37843020487248685409…05031079553724586561

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

7.568 × 10¹⁰¹(102-digit number)

75686040974497370818…10062159107449173119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.568 × 10¹⁰¹(102-digit number)

75686040974497370818…10062159107449173121

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 #395,145

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