Block #305,921

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 6:16:13 PM · Difficulty 9.9938 · 6,498,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e66ed5ca5e65b5a671a618ab863f4af91589d482963c8dc3fb5a6a12a0107caf

View on Chainz ↗

Height

#305,921

Difficulty

9.993752

Transactions

Size

209 B

Version

Bits

09fe6683

Nonce

4,914

Timestamp

12/11/2013, 6:16:13 PM

Confirmations

6,498,398

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4e97c71d8ef3d3abf38c728068fe704664bc4640c0ae042f07c774b0f1620f25

Transactions (1)

Coinbase4e97c71d8ef3d3…c774b0f1620f25

1 in → 1 out10.0000 XPM116 B

AbwWkWZt…kawDhufa

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.

2.724 × 10¹⁰²(103-digit number)

27247298209894483475…13719232345355059199

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

2.724 × 10¹⁰²(103-digit number)

27247298209894483475…13719232345355059199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.724 × 10¹⁰²(103-digit number)

27247298209894483475…13719232345355059201

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

5.449 × 10¹⁰²(103-digit number)

54494596419788966950…27438464690710118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.449 × 10¹⁰²(103-digit number)

54494596419788966950…27438464690710118401

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

1.089 × 10¹⁰³(104-digit number)

10898919283957793390…54876929381420236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.089 × 10¹⁰³(104-digit number)

10898919283957793390…54876929381420236801

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

2.179 × 10¹⁰³(104-digit number)

21797838567915586780…09753858762840473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.179 × 10¹⁰³(104-digit number)

21797838567915586780…09753858762840473601

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

4.359 × 10¹⁰³(104-digit number)

43595677135831173560…19507717525680947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.359 × 10¹⁰³(104-digit number)

43595677135831173560…19507717525680947201

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