Block #456,620

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 8:36:31 AM · Difficulty 10.4175 · 6,338,764 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c10f9f936a5f2054233123686ce8176acc4bc1553cf618572ff37e1b64473c9e

View on Chainz ↗

Height

#456,620

Difficulty

10.417481

Transactions

Size

2.11 KB

Version

Bits

0a6ae010

Nonce

377,678

Timestamp

3/23/2014, 8:36:31 AM

Confirmations

6,338,764

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0bd3a48b7482dc693161faab32dd8108b5ec55f9d6230b42da3c3c4774ca914f

Transactions (5)

Coinbase88c5de87083a52…4ccf642699a6f8

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

0a3cdadf7c7a26…ceeee45d333309

5 in → 2 out25.0258 XPM818 B

AJZjttDr…6kERQ243 AGoTUBFi…8RMus46w

16b7a7a9eab7f1…3ea513dcea6453

3 in → 2 out10.2077 XPM521 B

AHyPjTae…S7D2ctZm AJJu16ii…1zZTWnqc

54856835a94c9c…9a890485d4a643

1 in → 7 out14.9666 XPM397 B

AHoENRJk…NhmYqijD AdBaic4X…J8FiPQui Admcp7uW…Z5LZP5bN AVHcc9zb…JkngbvXL AVg5YGji…Aq7MMxRC

785ec08c1e8143…947363865646e8

1 in → 2 out7.2054 XPM227 B

AbE4r7MY…Q3pptGQk ALmMsp2G…xmrJ762X

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.

1.330 × 10⁹⁸(99-digit number)

13301096369967381103…11162022970607587839

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

1.330 × 10⁹⁸(99-digit number)

13301096369967381103…11162022970607587839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.330 × 10⁹⁸(99-digit number)

13301096369967381103…11162022970607587841

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

2.660 × 10⁹⁸(99-digit number)

26602192739934762206…22324045941215175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.660 × 10⁹⁸(99-digit number)

26602192739934762206…22324045941215175681

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

5.320 × 10⁹⁸(99-digit number)

53204385479869524413…44648091882430351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.320 × 10⁹⁸(99-digit number)

53204385479869524413…44648091882430351361

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

1.064 × 10⁹⁹(100-digit number)

10640877095973904882…89296183764860702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.064 × 10⁹⁹(100-digit number)

10640877095973904882…89296183764860702721

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

2.128 × 10⁹⁹(100-digit number)

21281754191947809765…78592367529721405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.128 × 10⁹⁹(100-digit number)

21281754191947809765…78592367529721405441

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