Block #2,447,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2017, 5:12:45 AM · Difficulty 10.9438 · 4,386,562 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b34367260e3bd97527b9f404fea3e6f308da29d50357c28ef9ed43eb67f8ad7

View on Chainz ↗

Height

#2,447,179

Difficulty

10.943768

Transactions

Size

6.10 KB

Version

Bits

0af19acf

Nonce

347,180,684

Timestamp

12/29/2017, 5:12:45 AM

Confirmations

4,386,562

Mined by

⛏️ P2SHAYT7mzh5iyzmaXkN47ZkjUH9syZ9N1Z1nC

Merkle Root

6cc52440d0cd74fb7128b2f82b8564b57705575750115b5191454f44196a8c3f

Transactions (3)

Coinbasee6a8d0127f7ea0…342ecf6c4c9941

1 in → 1 out8.4200 XPM110 B

AYT7mzh5…Z9N1Z1nC

70e1c24e68f3bd…09d5dd995963aa

1 in → 2 out8.3400 XPM192 B

AeNHmQiu…umFa2KZQ ANxNfXmZ…4p5PaHCM

f5ef393eecc01a…7981f6e0095640

39 in → 2 out219.9105 XPM5.71 KB

AXnG7fjW…SJhVysuL AHEZ8ZzW…3MbuBo7T

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.

4.769 × 10⁹⁸(99-digit number)

47692211978608883873…63210843648011796479

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

4.769 × 10⁹⁸(99-digit number)

47692211978608883873…63210843648011796479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.769 × 10⁹⁸(99-digit number)

47692211978608883873…63210843648011796481

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

9.538 × 10⁹⁸(99-digit number)

95384423957217767747…26421687296023592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.538 × 10⁹⁸(99-digit number)

95384423957217767747…26421687296023592961

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

1.907 × 10⁹⁹(100-digit number)

19076884791443553549…52843374592047185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.907 × 10⁹⁹(100-digit number)

19076884791443553549…52843374592047185921

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

3.815 × 10⁹⁹(100-digit number)

38153769582887107098…05686749184094371839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.815 × 10⁹⁹(100-digit number)

38153769582887107098…05686749184094371841

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

7.630 × 10⁹⁹(100-digit number)

76307539165774214197…11373498368188743679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.630 × 10⁹⁹(100-digit number)

76307539165774214197…11373498368188743681

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 #2,447,179

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