Block #385,038

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 12:50:17 PM · Difficulty 10.4025 · 6,441,537 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83763eca4a339f046850088cdfa698bd77772eeae426bf7c8d6631955b0304bc

View on Chainz ↗

Height

#385,038

Difficulty

10.402535

Transactions

Size

1.81 KB

Version

Bits

0a670c82

Nonce

171,489

Timestamp

2/1/2014, 12:50:17 PM

Confirmations

6,441,537

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fb95b3e24f1ad3029bb2009cef91ddb3446ede3030ae3b87f190607ff773874a

Transactions (5)

Coinbase8dfea5572592bb…ff431db0e4983e

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

8ef8f56c75c927…aec7584cbffad0

1 in → 2 out5.6625 XPM226 B

ASRBjmKN…qmWTUbvb ALK1wML4…1ABPN7VE

d1f89b6b54d126…5922221f6f2010

1 in → 2 out5.0948 XPM226 B

AZ4vQEb5…k7Li1iHB AZvWsaAY…VadzYBsv

e7b462135bce12…e3832b7fb00a71

1 in → 2 out2.1064 XPM226 B

AcfFXRr4…V8DaPt3C Aa7yJdtx…roF1vrRx

b0822093dbe3bd…f97a94e3dbfedb

6 in → 2 out2.5300 XPM968 B

AQzhLeUG…u69kNqYm AVcHdq3H…GA7Y919T

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.

4.209 × 10⁹⁸(99-digit number)

42090186566318530859…43296827369610044439

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

4.209 × 10⁹⁸(99-digit number)

42090186566318530859…43296827369610044439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.209 × 10⁹⁸(99-digit number)

42090186566318530859…43296827369610044441

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

8.418 × 10⁹⁸(99-digit number)

84180373132637061718…86593654739220088879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.418 × 10⁹⁸(99-digit number)

84180373132637061718…86593654739220088881

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

1.683 × 10⁹⁹(100-digit number)

16836074626527412343…73187309478440177759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.683 × 10⁹⁹(100-digit number)

16836074626527412343…73187309478440177761

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

3.367 × 10⁹⁹(100-digit number)

33672149253054824687…46374618956880355519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.367 × 10⁹⁹(100-digit number)

33672149253054824687…46374618956880355521

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

6.734 × 10⁹⁹(100-digit number)

67344298506109649375…92749237913760711039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.734 × 10⁹⁹(100-digit number)

67344298506109649375…92749237913760711041

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 #385,038

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