Block #270,675

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 3:04:28 AM · Difficulty 9.9517 · 6,521,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dfa3de78872843c0a674cb1fde8e969b02e893b757fc9545ffa30d8ca5e149b3

View on Chainz ↗

Height

#270,675

Difficulty

9.951654

Transactions

Size

2.00 KB

Version

Bits

09f39fa1

Nonce

521,832

Timestamp

11/24/2013, 3:04:28 AM

Confirmations

6,521,060

Merkle Root

5b1275517cfb35bdd1f3c2b65dfff7d494d4a4775671e9b831b932f8a8e95e60

Transactions (4)

Coinbase115ba7f55f3739…d4fd5d2759df44

1 in → 1 out10.1100 XPM100 B

AbGkvdxH…oihMdBXd

f8f1adb4cb6f7c…855ff6c8efd879

2 in → 2 out91.0100 XPM375 B

AVjMipmM…JLnXSrZn AeLo3idy…3UjxF275

7f589e4aba2ef3…d9a6c4d7a23775

4 in → 2 out87.0100 XPM668 B

AeLo3idy…3UjxF275 ANFGTHmk…RqV3xZJN

fda2c70c7d5ad2…1bff752a1f284c

5 in → 2 out20.9103 XPM819 B

AHhWe44Z…JEcY8x14 AUJ6Wojo…U5ip9hMN

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.

1.058 × 10⁹³(94-digit number)

10580811129718315799…68455373801728235519

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

1.058 × 10⁹³(94-digit number)

10580811129718315799…68455373801728235519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.058 × 10⁹³(94-digit number)

10580811129718315799…68455373801728235521

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

2.116 × 10⁹³(94-digit number)

21161622259436631599…36910747603456471039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.116 × 10⁹³(94-digit number)

21161622259436631599…36910747603456471041

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

4.232 × 10⁹³(94-digit number)

42323244518873263199…73821495206912942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.232 × 10⁹³(94-digit number)

42323244518873263199…73821495206912942081

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

8.464 × 10⁹³(94-digit number)

84646489037746526398…47642990413825884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.464 × 10⁹³(94-digit number)

84646489037746526398…47642990413825884161

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

1.692 × 10⁹⁴(95-digit number)

16929297807549305279…95285980827651768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.692 × 10⁹⁴(95-digit number)

16929297807549305279…95285980827651768321

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