Block #440,488

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 11:17:38 AM · Difficulty 10.3524 · 6,366,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa97a66d2ed2145d3198cd647060ba4204764becff324a279559eccac88fb51a

View on Chainz ↗

Height

#440,488

Difficulty

10.352372

Transactions

Size

2.18 KB

Version

Bits

0a5a350f

Nonce

33,223

Timestamp

3/12/2014, 11:17:38 AM

Confirmations

6,366,700

Mined by

⛏️ oAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1d0c1933750badfb242460b7653d49b9debe1e5a2ad13764ad651b4e2b11cf7c

Transactions (3)

Coinbasef9d8c2caee0a5f…a5e3f6719d2431

1 in → 21 out9.3400 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AbHY4iza…Yckt2J5W AdoqUYAy…tJ482T9b AVSSoqRA…aFjFn3Zm

5421e9685e72fa…10c1f66976cd83

3 in → 9 out24.9708 XPM694 B

AeKNrjNj…1NEq95Ta ATPcT4hy…BWv2Trvr AL7194fk…YNQBVjTB AbABGh95…BpJH6dHp AXDEZh15…FbrAPGkC

2f65b85f59e281…69b1f3e78de6c4

4 in → 2 out1.3234 XPM669 B

ATzNqULc…5WQcwDbE AJpPwFEs…NdefVvWm

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.

2.733 × 10⁹⁷(98-digit number)

27337799457712566278…92545896946899360379

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

2.733 × 10⁹⁷(98-digit number)

27337799457712566278…92545896946899360379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.733 × 10⁹⁷(98-digit number)

27337799457712566278…92545896946899360381

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

5.467 × 10⁹⁷(98-digit number)

54675598915425132556…85091793893798720759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.467 × 10⁹⁷(98-digit number)

54675598915425132556…85091793893798720761

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

1.093 × 10⁹⁸(99-digit number)

10935119783085026511…70183587787597441519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.093 × 10⁹⁸(99-digit number)

10935119783085026511…70183587787597441521

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

2.187 × 10⁹⁸(99-digit number)

21870239566170053022…40367175575194883039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.187 × 10⁹⁸(99-digit number)

21870239566170053022…40367175575194883041

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

4.374 × 10⁹⁸(99-digit number)

43740479132340106045…80734351150389766079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.374 × 10⁹⁸(99-digit number)

43740479132340106045…80734351150389766081

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 #440,488

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