Block #282,847

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 12:53:28 PM · Difficulty 9.9800 · 6,533,641 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

667b0aede2cf633083bd1c5ed994ce63211a5320a0c3037b534dea157ac0fc91

View on Chainz ↗

Height

#282,847

Difficulty

9.979969

Transactions

Size

1.18 KB

Version

Bits

09fadf3b

Nonce

46,576

Timestamp

11/29/2013, 12:53:28 PM

Confirmations

6,533,641

Mined by

⛏️ PaR>AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

d5fc4e6e8496654542fa58c4764f2b99d5eb36d289729e8e04a0ed0f44cfff3e

Transactions (1)

Coinbased5fc4e6e849665…a0ed0f44cfff3e

1 in → 31 out10.0100 XPM1.09 KB

AGFAJ5YL…ZEnBbk6G AaN3X4nJ…7DX2KLvh Ac6mGvmQ…XqWmPHjR AJzWx2VD…j4ZSMit5 AZ2pPuKg…95SN2Yr7

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.

3.875 × 10⁸⁸(89-digit number)

38750499281221674578…56409918012331175089

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

3.875 × 10⁸⁸(89-digit number)

38750499281221674578…56409918012331175089

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.875 × 10⁸⁸(89-digit number)

38750499281221674578…56409918012331175091

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

7.750 × 10⁸⁸(89-digit number)

77500998562443349156…12819836024662350179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.750 × 10⁸⁸(89-digit number)

77500998562443349156…12819836024662350181

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

1.550 × 10⁸⁹(90-digit number)

15500199712488669831…25639672049324700359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.550 × 10⁸⁹(90-digit number)

15500199712488669831…25639672049324700361

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

3.100 × 10⁸⁹(90-digit number)

31000399424977339662…51279344098649400719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.100 × 10⁸⁹(90-digit number)

31000399424977339662…51279344098649400721

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

6.200 × 10⁸⁹(90-digit number)

62000798849954679325…02558688197298801439

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 #282,847

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