Block #146,133

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 7:42:48 AM · Difficulty 9.8470 · 6,671,088 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

160899c93bd7b041a0c81c1c0a0681c0c1bc75324f2acaf1a5d88c1cda804756

View on Chainz ↗

Height

#146,133

Difficulty

9.847029

Transactions

Size

722 B

Version

Bits

09d8d6ea

Nonce

23,144

Timestamp

9/2/2013, 7:42:48 AM

Confirmations

6,671,088

Mined by

⛏️ P2SHAbViMiuJnu5b249sJfyEXnEpk8sQohmRvT

Merkle Root

9f9f8445e88889f25025c5765ed833274386113f61d1fb574b7a6fec2d12ca45

Transactions (2)

Coinbasef1e58fc9fe4f2f…367f3f270213eb

1 in → 1 out10.3100 XPM109 B

AbViMiuJ…sQohmRvT

146760b48ab0a1…40619849d3f472

3 in → 2 out208.7303 XPM524 B

AYtMiX9E…Q2uYCGgD ATn7bwu3…oMc5gvDW

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.

4.121 × 10⁹¹(92-digit number)

41210000615732732677…57641007248316327969

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

4.121 × 10⁹¹(92-digit number)

41210000615732732677…57641007248316327969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.121 × 10⁹¹(92-digit number)

41210000615732732677…57641007248316327971

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

8.242 × 10⁹¹(92-digit number)

82420001231465465354…15282014496632655939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.242 × 10⁹¹(92-digit number)

82420001231465465354…15282014496632655941

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

1.648 × 10⁹²(93-digit number)

16484000246293093070…30564028993265311879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.648 × 10⁹²(93-digit number)

16484000246293093070…30564028993265311881

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

3.296 × 10⁹²(93-digit number)

32968000492586186141…61128057986530623759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.296 × 10⁹²(93-digit number)

32968000492586186141…61128057986530623761

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

6.593 × 10⁹²(93-digit number)

65936000985172372283…22256115973061247519

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 #146,133

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