Block #300,404

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/8/2013, 2:00:48 PM · Difficulty 9.9923 · 6,509,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8721960e9650acd0d216e0aaa3d7df4e311d5dc9f843c6781e00ca7bfb0a2a4

View on Chainz ↗

Height

#300,404

Difficulty

9.992285

Transactions

Size

1.11 KB

Version

Bits

09fe065f

Nonce

94,676

Timestamp

12/8/2013, 2:00:48 PM

Confirmations

6,509,927

Mined by

⛏️ taRzOAcM3ext6YRUPiXDZcQabLFkVZmHwtj9Qp3

Merkle Root

be49321a08bca9896c958dc3dbd543808ed738b113235084bf6459f62c96acdd

Transactions (1)

Coinbasebe49321a08bca9…6459f62c96acdd

1 in → 29 out9.9800 XPM1.02 KB

AcM3ext6…Hwtj9Qp3 Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops Acs9SHrk…QJSB8SFG AZ2pPuKg…95SN2Yr7

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.

3.171 × 10⁹⁷(98-digit number)

31712316026468466859…61178690800149354219

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

3.171 × 10⁹⁷(98-digit number)

31712316026468466859…61178690800149354219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.171 × 10⁹⁷(98-digit number)

31712316026468466859…61178690800149354221

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

6.342 × 10⁹⁷(98-digit number)

63424632052936933719…22357381600298708439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.342 × 10⁹⁷(98-digit number)

63424632052936933719…22357381600298708441

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

1.268 × 10⁹⁸(99-digit number)

12684926410587386743…44714763200597416879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.268 × 10⁹⁸(99-digit number)

12684926410587386743…44714763200597416881

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

2.536 × 10⁹⁸(99-digit number)

25369852821174773487…89429526401194833759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.536 × 10⁹⁸(99-digit number)

25369852821174773487…89429526401194833761

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

5.073 × 10⁹⁸(99-digit number)

50739705642349546975…78859052802389667519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.073 × 10⁹⁸(99-digit number)

50739705642349546975…78859052802389667521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.014 × 10⁹⁹(100-digit number)

10147941128469909395…57718105604779335039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #300,404

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