Block #268,223

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 10:48:19 PM · Difficulty 9.9577 · 6,545,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8fcdb5318e17f9ba8e330c1e846d80e403565e97028327c33f88c35e1b5764f

View on Chainz ↗

Height

#268,223

Difficulty

9.957679

Transactions

Size

1.91 KB

Version

Bits

09f52a7a

Nonce

461,843

Timestamp

11/21/2013, 10:48:19 PM

Confirmations

6,545,621

Mined by

⛏️ aR_AQyr8Lw3A4nTbkdHcAPqKiPptkhs4nt3Pn

Merkle Root

ba872909c532001e82113cca378d804d37c20886b35c1cc186eb177d94ed02f6

Transactions (1)

Coinbaseba872909c53200…eb177d94ed02f6

1 in → 53 out10.0500 XPM1.82 KB

AQyr8Lw3…hs4nt3Pn AFqKfjez…qX9Ace3g AKXeSXzu…yeuNjvhB AdnG9gQ7…N9B7mA2p ANuKx9Ke…wm7nrBRq

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.

3.036 × 10⁹¹(92-digit number)

30368248262641743001…96913726584758474719

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

3.036 × 10⁹¹(92-digit number)

30368248262641743001…96913726584758474719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.036 × 10⁹¹(92-digit number)

30368248262641743001…96913726584758474721

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

6.073 × 10⁹¹(92-digit number)

60736496525283486002…93827453169516949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.073 × 10⁹¹(92-digit number)

60736496525283486002…93827453169516949441

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

1.214 × 10⁹²(93-digit number)

12147299305056697200…87654906339033898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.214 × 10⁹²(93-digit number)

12147299305056697200…87654906339033898881

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

2.429 × 10⁹²(93-digit number)

24294598610113394401…75309812678067797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.429 × 10⁹²(93-digit number)

24294598610113394401…75309812678067797761

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

4.858 × 10⁹²(93-digit number)

48589197220226788802…50619625356135595519

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 #268,223

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