Block #411,195

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 2:07:17 PM · Difficulty 10.4314 · 6,379,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c347b2bb12b996126a20b9fdfc4b93446b02cdb8eeb9ad3c6ef691ca2ac9e680

View on Chainz ↗

Height

#411,195

Difficulty

10.431357

Transactions

Size

358 B

Version

Bits

0a6e6d64

Nonce

10,380,894

Timestamp

2/19/2014, 2:07:17 PM

Confirmations

6,379,945

Merkle Root

67ea474f367f4683f3633eb5b1481238c620597ded78bdd55133a93abe0e8042

Transactions (2)

Coinbase2347004b861327…e48be29809afa9

1 in → 1 out9.1900 XPM109 B

AXCY29q5…swwxoo4S

7407fada3ea8d5…88b788bff682a7

1 in → 1 out9.2500 XPM158 B

ATV4M1CV…dd9zw8nH

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.

4.244 × 10⁹⁶(97-digit number)

42446681269168215178…62419947262353177599

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

4.244 × 10⁹⁶(97-digit number)

42446681269168215178…62419947262353177599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.244 × 10⁹⁶(97-digit number)

42446681269168215178…62419947262353177601

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

8.489 × 10⁹⁶(97-digit number)

84893362538336430356…24839894524706355199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.489 × 10⁹⁶(97-digit number)

84893362538336430356…24839894524706355201

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

1.697 × 10⁹⁷(98-digit number)

16978672507667286071…49679789049412710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.697 × 10⁹⁷(98-digit number)

16978672507667286071…49679789049412710401

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

3.395 × 10⁹⁷(98-digit number)

33957345015334572142…99359578098825420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.395 × 10⁹⁷(98-digit number)

33957345015334572142…99359578098825420801

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

6.791 × 10⁹⁷(98-digit number)

67914690030669144285…98719156197650841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.791 × 10⁹⁷(98-digit number)

67914690030669144285…98719156197650841601

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