Block #25,724

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 3:02:21 AM · Difficulty 7.9722 · 6,791,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8342151a85ff1bd615c4c6b23449c8f4fbb3a5d818158372b79024204903dca7

View on Chainz ↗

Height

#25,724

Difficulty

7.972156

Transactions

Size

354 B

Version

Bits

07f8df3b

Nonce

Timestamp

7/13/2013, 3:02:21 AM

Confirmations

6,791,716

Mined by

⛏️ P2SHAMSVmLczvqLDGCHmKpWja6S7MT8y3wdcLJ

Merkle Root

8624429bbcdd4dd4372644027bb08bd7b56f6f68d8af02f97c90b025f8e2c20b

Transactions (2)

Coinbase8cca3f2dbe54c5…94903bcc4bad85

1 in → 1 out15.7200 XPM108 B

AMSVmLcz…8y3wdcLJ

b3fed0a36ed25f…be2889f4df620e

1 in → 1 out15.7800 XPM157 B

AXPRySWh…GeFZKjLU

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.

6.758 × 10⁹¹(92-digit number)

67582477647771238052…43680772507059032199

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

6.758 × 10⁹¹(92-digit number)

67582477647771238052…43680772507059032199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.758 × 10⁹¹(92-digit number)

67582477647771238052…43680772507059032201

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

1.351 × 10⁹²(93-digit number)

13516495529554247610…87361545014118064399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.351 × 10⁹²(93-digit number)

13516495529554247610…87361545014118064401

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

2.703 × 10⁹²(93-digit number)

27032991059108495221…74723090028236128799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.703 × 10⁹²(93-digit number)

27032991059108495221…74723090028236128801

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

5.406 × 10⁹²(93-digit number)

54065982118216990442…49446180056472257599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 #25,724

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