Block #445,588

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 12:05:26 AM · Difficulty 10.3572 · 6,362,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37272576a6d08e47a142451bf28ef7f2437a33942fcf6468ea4be7b366eccf8c

View on Chainz ↗

Height

#445,588

Difficulty

10.357171

Transactions

Size

1.01 KB

Version

Bits

0a5b6f95

Nonce

645

Timestamp

3/16/2014, 12:05:26 AM

Confirmations

6,362,448

Mined by

⛏️ aS$s`AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7d3fd2867f2d0e234ffdf1bde18ecd92423edfee6e67a716f9a6f66fff4972aa

Transactions (1)

Coinbase7d3fd2867f2d0e…a6f66fff4972aa

1 in → 26 out9.3100 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR

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.

6.539 × 10⁹⁴(95-digit number)

65398560352258804203…41991977368598420479

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

6.539 × 10⁹⁴(95-digit number)

65398560352258804203…41991977368598420479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.539 × 10⁹⁴(95-digit number)

65398560352258804203…41991977368598420481

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

1.307 × 10⁹⁵(96-digit number)

13079712070451760840…83983954737196840959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.307 × 10⁹⁵(96-digit number)

13079712070451760840…83983954737196840961

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

2.615 × 10⁹⁵(96-digit number)

26159424140903521681…67967909474393681919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.615 × 10⁹⁵(96-digit number)

26159424140903521681…67967909474393681921

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

5.231 × 10⁹⁵(96-digit number)

52318848281807043362…35935818948787363839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.231 × 10⁹⁵(96-digit number)

52318848281807043362…35935818948787363841

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

1.046 × 10⁹⁶(97-digit number)

10463769656361408672…71871637897574727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.046 × 10⁹⁶(97-digit number)

10463769656361408672…71871637897574727681

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 #445,588

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