Block #230,800

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 1:13:45 AM · Difficulty 9.9399 · 6,578,978 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bfb1dd55eeb5edf3bea4b588a948124b19ef90fa68a90cc6335ef643e5f47c26

View on Chainz ↗

Height

#230,800

Difficulty

9.939852

Transactions

Size

1.36 KB

Version

Bits

09f09a26

Nonce

15,781

Timestamp

10/28/2013, 1:13:45 AM

Confirmations

6,578,978

Mined by

⛏️ P2SHAWthjApz915PzsrEMt8kEw4Rxjhs8Kjx7u

Merkle Root

1a5724413b5476207a232be6e71f3f3f30460a0f7668822393f1cae8f7c69874

Transactions (3)

Coinbasee5bf9fafe1a6dd…7623ae50dd122a

1 in → 1 out10.1300 XPM109 B

AWthjApz…hs8Kjx7u

ffe4dfb27a4d54…89bfbc7ac4ac7c

5 in → 2 out41.5722 XPM819 B

AHRSjffZ…1UoAZFnY AQAvQSWZ…C9mFkvux

d1d6211e148ce5…c9d58b2030145f

2 in → 2 out3.0862 XPM376 B

AZz6Bg87…MZtiQn8U Ac8ZHr6s…7L2xQGHb

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.

1.272 × 10⁹⁰(91-digit number)

12723421137281049265…51639155516369561249

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

1.272 × 10⁹⁰(91-digit number)

12723421137281049265…51639155516369561249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.272 × 10⁹⁰(91-digit number)

12723421137281049265…51639155516369561251

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

2.544 × 10⁹⁰(91-digit number)

25446842274562098530…03278311032739122499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.544 × 10⁹⁰(91-digit number)

25446842274562098530…03278311032739122501

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

5.089 × 10⁹⁰(91-digit number)

50893684549124197060…06556622065478244999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.089 × 10⁹⁰(91-digit number)

50893684549124197060…06556622065478245001

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

1.017 × 10⁹¹(92-digit number)

10178736909824839412…13113244130956489999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.017 × 10⁹¹(92-digit number)

10178736909824839412…13113244130956490001

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

2.035 × 10⁹¹(92-digit number)

20357473819649678824…26226488261912979999

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 #230,800

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