Block #226,765

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/25/2013, 11:06:37 AM · Difficulty 9.9359 · 6,582,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfc0899b67f33f15f3d6208746eb07b7fefa3dfbf388214726bde269c0dc75b7

View on Chainz ↗

Height

#226,765

Difficulty

9.935890

Transactions

Size

986 B

Version

Bits

09ef967c

Nonce

159,046

Timestamp

10/25/2013, 11:06:37 AM

Confirmations

6,582,403

Mined by

⛏️ P2SHAZh37xLoZAaGvZ332vYhsgYFo5ADD1wQTs

Merkle Root

a584f307b92d30cf28d7bbe370c5e1ba980ed99f045c9ab979874622e7b8e041

Transactions (4)

Coinbase966290aec6ffec…59e25df3f7f370

1 in → 1 out10.1400 XPM109 B

AZh37xLo…ADD1wQTs

2faa25ebbdbe35…6ea08401be026b

1 in → 2 out10.1000 XPM190 B

ASTaVbEi…Ec1HS4dP AQAvQSWZ…C9mFkvux

6e3481d9549f6f…2ae760f7917e31

2 in → 2 out15.1624 XPM373 B

ASuoUi24…FwBoFbxd AcfY4FVd…mGzYqkcA

d32c273e7e2e48…2e7789d820786b

1 in → 2 out6.0181 XPM225 B

AXUYcNrW…AZLdNAei AMhdLHbY…6FS66kj2

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.

6.391 × 10⁹²(93-digit number)

63910781992613503440…51075433600864348159

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

6.391 × 10⁹²(93-digit number)

63910781992613503440…51075433600864348159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.391 × 10⁹²(93-digit number)

63910781992613503440…51075433600864348161

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

1.278 × 10⁹³(94-digit number)

12782156398522700688…02150867201728696319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.278 × 10⁹³(94-digit number)

12782156398522700688…02150867201728696321

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

2.556 × 10⁹³(94-digit number)

25564312797045401376…04301734403457392639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.556 × 10⁹³(94-digit number)

25564312797045401376…04301734403457392641

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

5.112 × 10⁹³(94-digit number)

51128625594090802752…08603468806914785279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.112 × 10⁹³(94-digit number)

51128625594090802752…08603468806914785281

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

1.022 × 10⁹⁴(95-digit number)

10225725118818160550…17206937613829570559

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 #226,765

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