Block #444,623

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/15/2014, 9:10:45 AM · Difficulty 10.3478 · 6,380,914 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b96100a33ab3bbfc270fe68ce0a4d22bc96546eb55985d60c73fe0b0c124c6fe

View on Chainz ↗

Height

#444,623

Difficulty

10.347757

Transactions

Size

866 B

Version

Bits

0a590694

Nonce

86,699

Timestamp

3/15/2014, 9:10:45 AM

Confirmations

6,380,914

Mined by

⛏️ aS$yAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

97910a1622fbbf53d1a018598e12032879a56975ce2d78494cfcec7f5d331b93

Transactions (1)

Coinbase97910a1622fbbf…fcec7f5d331b93

1 in → 21 out9.3200 XPM776 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

3.250 × 10⁹⁵(96-digit number)

32504758641397141926…78871952444317609759

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

3.250 × 10⁹⁵(96-digit number)

32504758641397141926…78871952444317609759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.250 × 10⁹⁵(96-digit number)

32504758641397141926…78871952444317609761

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

6.500 × 10⁹⁵(96-digit number)

65009517282794283852…57743904888635219519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.500 × 10⁹⁵(96-digit number)

65009517282794283852…57743904888635219521

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

1.300 × 10⁹⁶(97-digit number)

13001903456558856770…15487809777270439039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.300 × 10⁹⁶(97-digit number)

13001903456558856770…15487809777270439041

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

2.600 × 10⁹⁶(97-digit number)

26003806913117713540…30975619554540878079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.600 × 10⁹⁶(97-digit number)

26003806913117713540…30975619554540878081

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

5.200 × 10⁹⁶(97-digit number)

52007613826235427081…61951239109081756159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.200 × 10⁹⁶(97-digit number)

52007613826235427081…61951239109081756161

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.040 × 10⁹⁷(98-digit number)

10401522765247085416…23902478218163512319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #444,623

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