Block #300,684

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 5:47:33 PM · Difficulty 9.9924 · 6,508,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

795b76b7e6251add05ce5b8a8156d1be647e0bc591d234e3a3431b0b7cb2fca7

View on Chainz ↗

Height

#300,684

Difficulty

9.992376

Transactions

Size

969 B

Version

Bits

09fe0c5f

Nonce

553,788

Timestamp

12/8/2013, 5:47:33 PM

Confirmations

6,508,792

Mined by

⛏️ aR\0AG3Vgv3wWQGbwqaAadK9FyXVz8fja3rCeH

Merkle Root

25a99cd6d87e28f75cd6b96e92060343906027b209002626123f449e070a1cfe

Transactions (1)

Coinbase25a99cd6d87e28…3f449e070a1cfe

1 in → 24 out10.0000 XPM879 B

AG3Vgv3w…fja3rCeH AKXeSXzu…yeuNjvhB AJBcbz2C…z57JquCp AYtDvcGs…VuAcA7m7 AQf7sjuh…sNY5fXpu

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.

6.115 × 10⁹³(94-digit number)

61155246534326809614…67859910839083366399

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

6.115 × 10⁹³(94-digit number)

61155246534326809614…67859910839083366399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.115 × 10⁹³(94-digit number)

61155246534326809614…67859910839083366401

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

1.223 × 10⁹⁴(95-digit number)

12231049306865361922…35719821678166732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.223 × 10⁹⁴(95-digit number)

12231049306865361922…35719821678166732801

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

2.446 × 10⁹⁴(95-digit number)

24462098613730723845…71439643356333465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.446 × 10⁹⁴(95-digit number)

24462098613730723845…71439643356333465601

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

4.892 × 10⁹⁴(95-digit number)

48924197227461447691…42879286712666931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.892 × 10⁹⁴(95-digit number)

48924197227461447691…42879286712666931201

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

9.784 × 10⁹⁴(95-digit number)

97848394454922895383…85758573425333862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.784 × 10⁹⁴(95-digit number)

97848394454922895383…85758573425333862401

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 #300,684

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