Block #273,143

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 3:47:47 PM · Difficulty 9.9542 · 6,536,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e04e3816ecddf452c4c41c365387c955268f60bcc36ba268d23aec4c6bf6af2

View on Chainz ↗

Height

#273,143

Difficulty

9.954191

Transactions

Size

1003 B

Version

Bits

09f445e0

Nonce

122,392

Timestamp

11/25/2013, 3:47:47 PM

Confirmations

6,536,544

Mined by

⛏️ *aRpAc5sZcdPRNjfrTK9pchLQrJN4XkzV4eckG

Merkle Root

0771e5efc2f2dfe5f72209e768cb1d0e80ad7e7826c0a394d69517be2f950934

Transactions (1)

Coinbase0771e5efc2f2df…9517be2f950934

1 in → 25 out10.0800 XPM913 B

Ac5sZcdP…kzV4eckG AMBbmvEz…yFqmSmw2 ANo4YY1x…vnsPRDSU ALdHh27b…XNbqrvPf AX6xJioT…NymntK8m

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.

5.082 × 10⁹⁵(96-digit number)

50825498140275498232…11336983386408837119

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

5.082 × 10⁹⁵(96-digit number)

50825498140275498232…11336983386408837119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.082 × 10⁹⁵(96-digit number)

50825498140275498232…11336983386408837121

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

1.016 × 10⁹⁶(97-digit number)

10165099628055099646…22673966772817674239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.016 × 10⁹⁶(97-digit number)

10165099628055099646…22673966772817674241

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

2.033 × 10⁹⁶(97-digit number)

20330199256110199292…45347933545635348479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.033 × 10⁹⁶(97-digit number)

20330199256110199292…45347933545635348481

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

4.066 × 10⁹⁶(97-digit number)

40660398512220398585…90695867091270696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.066 × 10⁹⁶(97-digit number)

40660398512220398585…90695867091270696961

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

8.132 × 10⁹⁶(97-digit number)

81320797024440797171…81391734182541393919

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 #273,143

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