Block #418,898

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 5:45:41 AM · Difficulty 10.3838 · 6,394,944 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd2d8b5b59c4f32805ff4ee615c32e4456449ca39a7523b6debb0b6722e1cab8

View on Chainz ↗

Height

#418,898

Difficulty

10.383796

Transactions

Size

833 B

Version

Bits

0a62407c

Nonce

176

Timestamp

2/25/2014, 5:45:41 AM

Confirmations

6,394,944

Mined by

⛏️ RdaS-gAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7c8ab7af17a49275fae433152df13a3b72af4564e9b91fc3cb920baa382a1983

Transactions (1)

Coinbase7c8ab7af17a492…920baa382a1983

1 in → 20 out9.2600 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

2.125 × 10⁹⁵(96-digit number)

21250170762887840443…35304035196951489919

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

2.125 × 10⁹⁵(96-digit number)

21250170762887840443…35304035196951489919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.125 × 10⁹⁵(96-digit number)

21250170762887840443…35304035196951489921

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

4.250 × 10⁹⁵(96-digit number)

42500341525775680886…70608070393902979839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.250 × 10⁹⁵(96-digit number)

42500341525775680886…70608070393902979841

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

8.500 × 10⁹⁵(96-digit number)

85000683051551361773…41216140787805959679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.500 × 10⁹⁵(96-digit number)

85000683051551361773…41216140787805959681

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

1.700 × 10⁹⁶(97-digit number)

17000136610310272354…82432281575611919359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.700 × 10⁹⁶(97-digit number)

17000136610310272354…82432281575611919361

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

3.400 × 10⁹⁶(97-digit number)

34000273220620544709…64864563151223838719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.400 × 10⁹⁶(97-digit number)

34000273220620544709…64864563151223838721

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 #418,898

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