Block #444,256

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 3:55:29 AM · Difficulty 10.3405 · 6,382,854 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7562935297309baa0be2d0e0b2f97f35adc4011578885b3c62843478acb70029

View on Chainz ↗

Height

#444,256

Difficulty

10.340545

Transactions

Size

1.17 KB

Version

Bits

0a572dfd

Nonce

12,929

Timestamp

3/15/2014, 3:55:29 AM

Confirmations

6,382,854

Mined by

⛏️ `aS#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8c12ffa9c75f957b9620a9a6f36d65f6d939f073ce773846ee5d175634444aa9

Transactions (2)

Coinbase4f1855f431c6b7…2f1f3bcf5990fa

1 in → 24 out9.3400 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AMm3qeod…8PBiCMXU

d53ff155aace02…22696741426238

1 in → 2 out2850.9593 XPM227 B

ASUZ2j3r…xMLKReLm ASwZPpjG…sET5nAqJ

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.

8.803 × 10⁹⁵(96-digit number)

88032981452659063947…98223767899199350879

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

8.803 × 10⁹⁵(96-digit number)

88032981452659063947…98223767899199350879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.803 × 10⁹⁵(96-digit number)

88032981452659063947…98223767899199350881

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

1.760 × 10⁹⁶(97-digit number)

17606596290531812789…96447535798398701759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.760 × 10⁹⁶(97-digit number)

17606596290531812789…96447535798398701761

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

3.521 × 10⁹⁶(97-digit number)

35213192581063625579…92895071596797403519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.521 × 10⁹⁶(97-digit number)

35213192581063625579…92895071596797403521

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

7.042 × 10⁹⁶(97-digit number)

70426385162127251158…85790143193594807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.042 × 10⁹⁶(97-digit number)

70426385162127251158…85790143193594807041

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

1.408 × 10⁹⁷(98-digit number)

14085277032425450231…71580286387189614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.408 × 10⁹⁷(98-digit number)

14085277032425450231…71580286387189614081

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 #444,256

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