Block #440,697

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 2:56:47 PM · Difficulty 10.3510 · 6,367,001 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1654a54f109b3b9fab848a68cc0047efe8c3153afa84ac6899c7bc1ce8a4c9c

View on Chainz ↗

Height

#440,697

Difficulty

10.350979

Transactions

Size

863 B

Version

Bits

0a59d9c0

Nonce

100,506

Timestamp

3/12/2014, 2:56:47 PM

Confirmations

6,367,001

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b27b7617a51b9be6b3f92ed6de42fb231c6f9e90d66ad7936b66f160f7d47552

Transactions (2)

Coinbasedc746218e09e0a…bc0e8b2d5eb98f

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

e20797ecf9b919…42314aebbdfdbd

3 in → 9 out27.9400 XPM656 B

APYNwjHe…933tHKZF AUqW9AoW…eBAK1fjh AcinGPZc…Y8oaD67T AQEx65ab…Sn8HJuB1 AcADmAoe…8iNnoMzB

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.

2.167 × 10⁹⁷(98-digit number)

21673678807089357755…39527347474946884139

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

2.167 × 10⁹⁷(98-digit number)

21673678807089357755…39527347474946884139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.167 × 10⁹⁷(98-digit number)

21673678807089357755…39527347474946884141

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

4.334 × 10⁹⁷(98-digit number)

43347357614178715511…79054694949893768279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.334 × 10⁹⁷(98-digit number)

43347357614178715511…79054694949893768281

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

8.669 × 10⁹⁷(98-digit number)

86694715228357431022…58109389899787536559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.669 × 10⁹⁷(98-digit number)

86694715228357431022…58109389899787536561

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

1.733 × 10⁹⁸(99-digit number)

17338943045671486204…16218779799575073119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.733 × 10⁹⁸(99-digit number)

17338943045671486204…16218779799575073121

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

3.467 × 10⁹⁸(99-digit number)

34677886091342972409…32437559599150146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.467 × 10⁹⁸(99-digit number)

34677886091342972409…32437559599150146241

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 #440,697

Cookie Preferences