Block #304,285

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 8:34:52 PM · Difficulty 9.9933 · 6,504,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

017119f1639e37a03acf8f9094341aeb5b32904d1667a0fe8d2efbbd8986f76f

View on Chainz ↗

Height

#304,285

Difficulty

9.993270

Transactions

Size

1.18 KB

Version

Bits

09fe46ec

Nonce

30,293

Timestamp

12/10/2013, 8:34:52 PM

Confirmations

6,504,433

Mined by

⛏️ aRzAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

edd516946b9f33e0472f031750db539cd4aae3520486e6b7fc91adf2f99206df

Transactions (1)

Coinbaseedd516946b9f33…91adf2f99206df

1 in → 31 out9.9800 XPM1.09 KB

AQwRN8bE…V8PsTcY9 AcC2zSod…rtWatH79 AN63YyQR…1tfe566A AYtDvcGs…VuAcA7m7 AWXYBWKP…qQAoisBJ

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.

4.190 × 10⁹³(94-digit number)

41901002284117543106…79044468608299234159

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

4.190 × 10⁹³(94-digit number)

41901002284117543106…79044468608299234159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.190 × 10⁹³(94-digit number)

41901002284117543106…79044468608299234161

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

8.380 × 10⁹³(94-digit number)

83802004568235086212…58088937216598468319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.380 × 10⁹³(94-digit number)

83802004568235086212…58088937216598468321

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

1.676 × 10⁹⁴(95-digit number)

16760400913647017242…16177874433196936639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.676 × 10⁹⁴(95-digit number)

16760400913647017242…16177874433196936641

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

3.352 × 10⁹⁴(95-digit number)

33520801827294034484…32355748866393873279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.352 × 10⁹⁴(95-digit number)

33520801827294034484…32355748866393873281

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

6.704 × 10⁹⁴(95-digit number)

67041603654588068969…64711497732787746559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #304,285

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