Block #284,840

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 6:53:55 AM · Difficulty 9.9833 · 6,546,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd5d4f50e12efab8b0c2d34bbebcc11c1426847140b7acbf4e7a6daa40af3c18

View on Chainz ↗

Height

#284,840

Difficulty

9.983350

Transactions

Size

3.79 KB

Version

Bits

09fbbcd0

Nonce

29,515

Timestamp

11/30/2013, 6:53:55 AM

Confirmations

6,546,255

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2485d75c41fb304dd181fd2642a02545c79a8a19e569d050c489296f0f0ca680

Transactions (5)

Coinbase0acb10b9f79eae…4c4b2cefb2c431

1 in → 1 out10.0800 XPM109 B

AeKNrjNj…1NEq95Ta

9c1deb97a30336…e5a9d84af5c960

1 in → 2 out2.6290 XPM227 B

ANxTdZg8…kUMGs75V ATNAKXn4…gNAq5i7m

bcc11d03e738ab…cdf8ae59186d50

19 in → 1 out5.1631 XPM2.79 KB

ARjzzjSp…V1sSS15g

3b9efb8f704d73…1fb83ee26edc9a

2 in → 2 out1.9825 XPM374 B

AGuByVAK…Y36X8a9Z AHaDgjUP…tjfE6C6M

e128e3ce3795c8…0537ca8e0eefca

1 in → 2 out5.6254 XPM225 B

Addvgs4U…Mm7xTUgb AKmEzHjw…DGNSyeZR

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.

5.081 × 10⁹³(94-digit number)

50816490900201316893…24254564802556245399

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

5.081 × 10⁹³(94-digit number)

50816490900201316893…24254564802556245399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.081 × 10⁹³(94-digit number)

50816490900201316893…24254564802556245401

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 × 10⁹⁴(95-digit number)

10163298180040263378…48509129605112490799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.016 × 10⁹⁴(95-digit number)

10163298180040263378…48509129605112490801

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

2.032 × 10⁹⁴(95-digit number)

20326596360080526757…97018259210224981599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.032 × 10⁹⁴(95-digit number)

20326596360080526757…97018259210224981601

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

4.065 × 10⁹⁴(95-digit number)

40653192720161053514…94036518420449963199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.065 × 10⁹⁴(95-digit number)

40653192720161053514…94036518420449963201

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

8.130 × 10⁹⁴(95-digit number)

81306385440322107029…88073036840899926399

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 #284,840

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