Block #425,349

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 8:41:21 PM · Difficulty 10.3608 · 6,416,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bdd30c0497936ada02b786649c1dc942db771872fc5f5f2f9c86335c90ba155

View on Chainz ↗

Height

#425,349

Difficulty

10.360780

Transactions

Size

1004 B

Version

Bits

0a5c5c13

Nonce

155,057

Timestamp

3/1/2014, 8:41:21 PM

Confirmations

6,416,550

Mined by

⛏️ }aSE-AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c176a1b621fe7f300f15345e7a5eb31add24674236e62befa219d9220041db39

Transactions (1)

Coinbasec176a1b621fe7f…19d9220041db39

1 in → 25 out9.3000 XPM913 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

7.208 × 10⁹⁵(96-digit number)

72080970352989556612…99828066323417976319

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

7.208 × 10⁹⁵(96-digit number)

72080970352989556612…99828066323417976319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.208 × 10⁹⁵(96-digit number)

72080970352989556612…99828066323417976321

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

1.441 × 10⁹⁶(97-digit number)

14416194070597911322…99656132646835952639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.441 × 10⁹⁶(97-digit number)

14416194070597911322…99656132646835952641

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

2.883 × 10⁹⁶(97-digit number)

28832388141195822644…99312265293671905279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.883 × 10⁹⁶(97-digit number)

28832388141195822644…99312265293671905281

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

5.766 × 10⁹⁶(97-digit number)

57664776282391645289…98624530587343810559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.766 × 10⁹⁶(97-digit number)

57664776282391645289…98624530587343810561

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

1.153 × 10⁹⁷(98-digit number)

11532955256478329057…97249061174687621119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.153 × 10⁹⁷(98-digit number)

11532955256478329057…97249061174687621121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #425,349

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