Block #2,285,133

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/6/2017, 4:08:53 PM · Difficulty 10.9553 · 4,545,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9955d9ce3f50d8648dab3221c761f8128fc1cf34ddc5d52795049f1143a75d4

View on Chainz ↗

Height

#2,285,133

Difficulty

10.955335

Transactions

Size

426 B

Version

Bits

0af490d3

Nonce

139,521,663

Timestamp

9/6/2017, 4:08:53 PM

Confirmations

4,545,857

Mined by

⛏️ P2SHAKaqsSCwa6SnviGSifiZExpmbs4a8LPq6V

Merkle Root

d621235135de4ec6cbf9e5fce82557cbbc91b20270c79acee820b574ad9c20d0

Transactions (2)

Coinbase0d54985fa22e9e…e0d593f6e4f92d

1 in → 1 out8.3300 XPM110 B

AKaqsSCw…4a8LPq6V

e5744744dfd84b…1d3b27cc9d33cd

1 in → 2 out1484.6602 XPM226 B

AS8Swa5k…emSJQqiE Aa12fnFH…hVG6PKXV

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.

4.792 × 10⁹⁵(96-digit number)

47928849855397499257…35928323733984335359

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

4.792 × 10⁹⁵(96-digit number)

47928849855397499257…35928323733984335359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.792 × 10⁹⁵(96-digit number)

47928849855397499257…35928323733984335361

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

9.585 × 10⁹⁵(96-digit number)

95857699710794998514…71856647467968670719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.585 × 10⁹⁵(96-digit number)

95857699710794998514…71856647467968670721

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

1.917 × 10⁹⁶(97-digit number)

19171539942158999702…43713294935937341439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.917 × 10⁹⁶(97-digit number)

19171539942158999702…43713294935937341441

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

3.834 × 10⁹⁶(97-digit number)

38343079884317999405…87426589871874682879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.834 × 10⁹⁶(97-digit number)

38343079884317999405…87426589871874682881

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

7.668 × 10⁹⁶(97-digit number)

76686159768635998811…74853179743749365759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.668 × 10⁹⁶(97-digit number)

76686159768635998811…74853179743749365761

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 #2,285,133

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