Block #2,641,743

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 11:32:45 AM · Difficulty 11.6300 · 4,201,254 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

848599516885ae8fbfa596cbbcdef4af42eac8345d3bba2637538b15f57b3511

View on Chainz ↗

Height

#2,641,743

Difficulty

11.630038

Transactions

Size

25.56 KB

Version

Bits

0ba14a2d

Nonce

1,916,635,309

Timestamp

5/1/2018, 11:32:45 AM

Confirmations

4,201,254

Mined by

⛏️ P2SHAPSv8LKuHefB1BHXzPmEEMf6kVUnVQYnF7

Merkle Root

76fee35e9db4caa5e6f0d29d7c7992d409ff3127e756e710b3c97d0d248566bc

Transactions (2)

Coinbase9d34f9893a59b3…17e240427767e4

1 in → 1 out7.6400 XPM110 B

APSv8LKu…UnVQYnF7

c2d497e58d1c45…7314f84533acff

175 in → 2 out2000.0132 XPM25.37 KB

APXuKVyb…2zEzh1jL AQRanRmJ…jnknhXJG

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.

3.436 × 10⁹⁷(98-digit number)

34362062703904586821…22292370804010352639

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

3.436 × 10⁹⁷(98-digit number)

34362062703904586821…22292370804010352639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.436 × 10⁹⁷(98-digit number)

34362062703904586821…22292370804010352641

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

6.872 × 10⁹⁷(98-digit number)

68724125407809173642…44584741608020705279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.872 × 10⁹⁷(98-digit number)

68724125407809173642…44584741608020705281

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

1.374 × 10⁹⁸(99-digit number)

13744825081561834728…89169483216041410559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.374 × 10⁹⁸(99-digit number)

13744825081561834728…89169483216041410561

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

2.748 × 10⁹⁸(99-digit number)

27489650163123669456…78338966432082821119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.748 × 10⁹⁸(99-digit number)

27489650163123669456…78338966432082821121

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

5.497 × 10⁹⁸(99-digit number)

54979300326247338913…56677932864165642239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.497 × 10⁹⁸(99-digit number)

54979300326247338913…56677932864165642241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.099 × 10⁹⁹(100-digit number)

10995860065249467782…13355865728331284479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,641,743

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