Block #281,453

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 12:53:16 AM · Difficulty 9.9771 · 6,529,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

176615b36723f914ff76488ecc1874f3a7c689d125b5b2f3ce05cacf47a6effb

View on Chainz ↗

Height

#281,453

Difficulty

9.977053

Transactions

Size

1.15 KB

Version

Bits

09fa2027

Nonce

16,528

Timestamp

11/29/2013, 12:53:16 AM

Confirmations

6,529,165

Mined by

⛏️ mKaRzAXLJzdRcD9MgvpKU9w362XbA8mLJLLZDBD

Merkle Root

1ba11d2e8cce265ddcea75b9cbc4def1da1015b9351abc953eeb4a37194efce9

Transactions (1)

Coinbase1ba11d2e8cce26…eb4a37194efce9

1 in → 30 out10.0100 XPM1.06 KB

AXLJzdRc…LJLLZDBD Acs9SHrk…QJSB8SFG AWZd1qVJ…9pj9yfPa AbtgNzNb…9Atvu81w AGFAJ5YL…ZEnBbk6G

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.

2.443 × 10⁹⁴(95-digit number)

24432875005710108123…77968484672318166159

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

2.443 × 10⁹⁴(95-digit number)

24432875005710108123…77968484672318166159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.443 × 10⁹⁴(95-digit number)

24432875005710108123…77968484672318166161

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

4.886 × 10⁹⁴(95-digit number)

48865750011420216247…55936969344636332319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.886 × 10⁹⁴(95-digit number)

48865750011420216247…55936969344636332321

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

9.773 × 10⁹⁴(95-digit number)

97731500022840432495…11873938689272664639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.773 × 10⁹⁴(95-digit number)

97731500022840432495…11873938689272664641

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

1.954 × 10⁹⁵(96-digit number)

19546300004568086499…23747877378545329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.954 × 10⁹⁵(96-digit number)

19546300004568086499…23747877378545329281

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

3.909 × 10⁹⁵(96-digit number)

39092600009136172998…47495754757090658559

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 #281,453

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