Block #184,132

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 11:26:44 AM · Difficulty 9.8592 · 6,633,174 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

039e63fd6436f01936ba0329a774306ca116cc2605432ec2ce64e222c85bda61

View on Chainz ↗

Height

#184,132

Difficulty

9.859194

Transactions

Size

1.72 KB

Version

Bits

09dbf421

Nonce

38,628

Timestamp

9/28/2013, 11:26:44 AM

Confirmations

6,633,174

Mined by

⛏️ P2SHAbKd1w8rR6WRGdSbm3U7vbLmmmxJthheuA

Merkle Root

f91a752ed2e0b77eb380247361d61044a71241bc62d60d793fadcffede464e6b

Transactions (4)

Coinbase0c3e0232c76970…73656855ceb693

1 in → 1 out10.3100 XPM109 B

AbKd1w8r…xJthheuA

34e972f92d953e…e938866f92c71d

1 in → 2 out10.2500 XPM226 B

AYWMgFep…7ovRUpmU AWTi6RZn…U7zZ1THp

fdafd49f6ef6aa…35bdfe491dc2ed

1 in → 2 out10.2500 XPM226 B

AKCvAf81…bmir7MN9 ANZqu5yG…TYXCnhNT

14840f2bd78c65…5108574a8b1a91

7 in → 2 out2.0285 XPM1.09 KB

ANsZYAZy…wSk4mkms AavxYuB8…zRRYmyvJ

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.

2.347 × 10⁹⁷(98-digit number)

23470987569375881138…91983666111156396159

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

2.347 × 10⁹⁷(98-digit number)

23470987569375881138…91983666111156396159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.347 × 10⁹⁷(98-digit number)

23470987569375881138…91983666111156396161

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

4.694 × 10⁹⁷(98-digit number)

46941975138751762276…83967332222312792319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.694 × 10⁹⁷(98-digit number)

46941975138751762276…83967332222312792321

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

9.388 × 10⁹⁷(98-digit number)

93883950277503524553…67934664444625584639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.388 × 10⁹⁷(98-digit number)

93883950277503524553…67934664444625584641

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

1.877 × 10⁹⁸(99-digit number)

18776790055500704910…35869328889251169279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.877 × 10⁹⁸(99-digit number)

18776790055500704910…35869328889251169281

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

3.755 × 10⁹⁸(99-digit number)

37553580111001409821…71738657778502338559

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 #184,132

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