Block #270,832

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 5:53:35 AM · Difficulty 9.9515 · 6,538,623 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b8840dfec728f75c310439378cb7ae9eafb9d7bdafe02137c1f7a16397163cc

View on Chainz ↗

Height

#270,832

Difficulty

9.951495

Transactions

Size

424 B

Version

Bits

09f39532

Nonce

19,357

Timestamp

11/24/2013, 5:53:35 AM

Confirmations

6,538,623

Mined by

⛏️ !aRnAGHJDQA6MYJdWVwCF6BCcGo8ZohCLcZMXq

Merkle Root

cc9ba353f94b0682c361509f0036ca982728eaf6a2802991940b7e2269d19225

Transactions (1)

Coinbasecc9ba353f94b06…0b7e2269d19225

1 in → 8 out10.0780 XPM335 B

AGHJDQA6…hCLcZMXq AKwqFUdz…D4jGNKFN AZT2M22K…rh3B6R9q AVVVLvhX…ShSvqxic AZDExdUo…sAaRkXPE

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.

1.163 × 10⁹³(94-digit number)

11639202055886531216…51632255423050703999

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

1.163 × 10⁹³(94-digit number)

11639202055886531216…51632255423050703999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.163 × 10⁹³(94-digit number)

11639202055886531216…51632255423050704001

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

2.327 × 10⁹³(94-digit number)

23278404111773062432…03264510846101407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.327 × 10⁹³(94-digit number)

23278404111773062432…03264510846101408001

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

4.655 × 10⁹³(94-digit number)

46556808223546124864…06529021692202815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.655 × 10⁹³(94-digit number)

46556808223546124864…06529021692202816001

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

9.311 × 10⁹³(94-digit number)

93113616447092249728…13058043384405631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.311 × 10⁹³(94-digit number)

93113616447092249728…13058043384405632001

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

1.862 × 10⁹⁴(95-digit number)

18622723289418449945…26116086768811263999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #270,832

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