Block #2,283,605

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/5/2017, 2:33:33 PM · Difficulty 10.9554 · 4,541,740 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d0773a509f0b1506b40998c0ac3b21ab49f6fa85aa80539c1abea08c41ffb858

View on Chainz ↗

Height

#2,283,605

Difficulty

10.955357

Transactions

Size

1.00 KB

Version

Bits

0af49248

Nonce

420,203,996

Timestamp

9/5/2017, 2:33:33 PM

Confirmations

4,541,740

Mined by

⛏️ P2SHATUggQcMDrnEAiGFqzBKo3KPic12uZnj8x

Merkle Root

3efcf03546ac151181c0cf3075c0d1fa087b12387dc7f9bae07d77c71edac101

Transactions (4)

Coinbasea318008c489796…c9209f595d0079

1 in → 1 out8.3500 XPM109 B

ATUggQcM…12uZnj8x

4cd9b82aacdd5e…b54f4a8b5f78de

1 in → 2 out62205.1723 XPM225 B

AHbn6HVw…pbdJZVYt AWVBJzri…1sMkuo1y

cec61e733ee6e3…4179b64321f357

1 in → 2 out21288.6335 XPM226 B

ARFFNRV9…vjxHHS3D AP34Fwig…UPDwnMw5

1ebdb897640fe2…64a47e6f8b7512

2 in → 2 out4.3370 XPM373 B

AcaVjMDj…EXYJhiCZ AJY8WoNm…xnXHCxVr

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.

3.362 × 10⁹⁶(97-digit number)

33623392488846874200…46028176385829253119

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

3.362 × 10⁹⁶(97-digit number)

33623392488846874200…46028176385829253119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.362 × 10⁹⁶(97-digit number)

33623392488846874200…46028176385829253121

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

6.724 × 10⁹⁶(97-digit number)

67246784977693748400…92056352771658506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.724 × 10⁹⁶(97-digit number)

67246784977693748400…92056352771658506241

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

1.344 × 10⁹⁷(98-digit number)

13449356995538749680…84112705543317012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.344 × 10⁹⁷(98-digit number)

13449356995538749680…84112705543317012481

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

2.689 × 10⁹⁷(98-digit number)

26898713991077499360…68225411086634024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.689 × 10⁹⁷(98-digit number)

26898713991077499360…68225411086634024961

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

5.379 × 10⁹⁷(98-digit number)

53797427982154998720…36450822173268049919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.379 × 10⁹⁷(98-digit number)

53797427982154998720…36450822173268049921

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 #2,283,605

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