Block #22,504

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 5:27:35 PM · Difficulty 7.9528 · 6,788,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b75b3718f135565eceefea8a8ebf0735b158d5afae2d7bf6e8423483d42450eb

View on Chainz ↗

Height

#22,504

Difficulty

7.952810

Transactions

Size

208 B

Version

Bits

07f3eb5c

Nonce

102

Timestamp

7/12/2013, 5:27:35 PM

Confirmations

6,788,580

Mined by

⛏️ P2SHALtQiCynzfouqbRxJ6ViGNCLqY68VU6xPK

Merkle Root

eb4623d37c58683a3184d384f4a584b0af44146c034107e69827036c43f9c845

Transactions (1)

Coinbaseeb4623d37c5868…27036c43f9c845

1 in → 1 out15.7900 XPM108 B

ALtQiCyn…68VU6xPK

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.

1.715 × 10¹¹⁸(119-digit number)

17155050016623632148…73201740136137171759

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

1.715 × 10¹¹⁸(119-digit number)

17155050016623632148…73201740136137171759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.715 × 10¹¹⁸(119-digit number)

17155050016623632148…73201740136137171761

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

3.431 × 10¹¹⁸(119-digit number)

34310100033247264296…46403480272274343519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.431 × 10¹¹⁸(119-digit number)

34310100033247264296…46403480272274343521

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

6.862 × 10¹¹⁸(119-digit number)

68620200066494528592…92806960544548687039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.862 × 10¹¹⁸(119-digit number)

68620200066494528592…92806960544548687041

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

1.372 × 10¹¹⁹(120-digit number)

13724040013298905718…85613921089097374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.372 × 10¹¹⁹(120-digit number)

13724040013298905718…85613921089097374081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #22,504

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