Block #300,332

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 1:02:03 PM · Difficulty 9.9923 · 6,509,997 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cf7903a3dfc2e3eba020323d9c42deb4ab2e412bec826b2e3a2451918b80805

View on Chainz ↗

Height

#300,332

Difficulty

9.992254

Transactions

Size

1.11 KB

Version

Bits

09fe0464

Nonce

62,962

Timestamp

12/8/2013, 1:02:03 PM

Confirmations

6,509,997

Mined by

⛏️ ,aRmAT1xr4ZBNvFhJPiF9xp6Bz1og93dcDkfYg

Merkle Root

179ef19534cffc7d8fdd81cebcfca785e883e29eb04c5c7fe7daee5da0dd239f

Transactions (1)

Coinbase179ef19534cffc…daee5da0dd239f

1 in → 29 out9.9800 XPM1.02 KB

AT1xr4ZB…3dcDkfYg Acs9SHrk…QJSB8SFG AHuJ9wYh…BGmgHrKZ AQf7sjuh…sNY5fXpu AUW89vJd…BiczGLRw

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.

3.486 × 10⁹⁵(96-digit number)

34866844432405345972…38885431064862736639

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

3.486 × 10⁹⁵(96-digit number)

34866844432405345972…38885431064862736639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.486 × 10⁹⁵(96-digit number)

34866844432405345972…38885431064862736641

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

6.973 × 10⁹⁵(96-digit number)

69733688864810691945…77770862129725473279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.973 × 10⁹⁵(96-digit number)

69733688864810691945…77770862129725473281

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

1.394 × 10⁹⁶(97-digit number)

13946737772962138389…55541724259450946559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.394 × 10⁹⁶(97-digit number)

13946737772962138389…55541724259450946561

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

2.789 × 10⁹⁶(97-digit number)

27893475545924276778…11083448518901893119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.789 × 10⁹⁶(97-digit number)

27893475545924276778…11083448518901893121

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

5.578 × 10⁹⁶(97-digit number)

55786951091848553556…22166897037803786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.578 × 10⁹⁶(97-digit number)

55786951091848553556…22166897037803786241

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 #300,332

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