Block #440,103

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 4:53:52 AM · Difficulty 10.3521 · 6,362,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

842ddfab51bc7f73bb212ee2c7261e3bb7d6c1473315d1327fbe8b791d516c15

View on Chainz ↗

Height

#440,103

Difficulty

10.352105

Transactions

Size

868 B

Version

Bits

0a5a2389

Nonce

38,874

Timestamp

3/12/2014, 4:53:52 AM

Confirmations

6,362,487

Mined by

⛏️ 'KAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

6e6df9e72b57ce4f09b0f08dc61608cd8096701e29ed4a50c8e5f6a6a79bbf8f

Transactions (1)

Coinbase6e6df9e72b57ce…e5f6a6a79bbf8f

1 in → 21 out9.3200 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AMW1p9oT…2TzdaZxH AcgDwGo8…BBFwbjVo

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.

1.794 × 10⁹⁷(98-digit number)

17948708439981804692…77968824697705605119

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

1.794 × 10⁹⁷(98-digit number)

17948708439981804692…77968824697705605119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.794 × 10⁹⁷(98-digit number)

17948708439981804692…77968824697705605121

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

3.589 × 10⁹⁷(98-digit number)

35897416879963609384…55937649395411210239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.589 × 10⁹⁷(98-digit number)

35897416879963609384…55937649395411210241

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

7.179 × 10⁹⁷(98-digit number)

71794833759927218768…11875298790822420479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.179 × 10⁹⁷(98-digit number)

71794833759927218768…11875298790822420481

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

1.435 × 10⁹⁸(99-digit number)

14358966751985443753…23750597581644840959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.435 × 10⁹⁸(99-digit number)

14358966751985443753…23750597581644840961

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

2.871 × 10⁹⁸(99-digit number)

28717933503970887507…47501195163289681919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.871 × 10⁹⁸(99-digit number)

28717933503970887507…47501195163289681921

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