Block #2,054,335

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2017, 10:35:42 AM · Difficulty 10.7915 · 4,785,540 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3e943102f0975e03489726467a83fcb7f895a1170d854e3989e346ed4dc6a75

View on Chainz ↗

Height

#2,054,335

Difficulty

10.791481

Transactions

Size

1.57 KB

Version

Bits

0aca9e80

Nonce

384,724,395

Timestamp

4/4/2017, 10:35:42 AM

Confirmations

4,785,540

Mined by

⛏️ P2SHAcWsu5KGCZ8TZmtQYrBgTgD4qDRVxELT3q

Merkle Root

1b08a6f7faa0cdba9cb2d5e50ba2e706e5d2d000a1f4c516ec58e53a064f74a9

Transactions (2)

Coinbaseafce16c5d6c367…1cf6cfd09d9fad

1 in → 1 out8.5900 XPM109 B

AcWsu5KG…RVxELT3q

13d6a9f6f6eac8…c8b0a1baff5f7a

9 in → 2 out1260.2827 XPM1.38 KB

ALMPewEv…QkLHqEuW ANPiaUVF…tNHpjMCq

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.

1.443 × 10⁹⁸(99-digit number)

14437502506456329063…96656079031385292799

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

1.443 × 10⁹⁸(99-digit number)

14437502506456329063…96656079031385292799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.443 × 10⁹⁸(99-digit number)

14437502506456329063…96656079031385292801

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

2.887 × 10⁹⁸(99-digit number)

28875005012912658127…93312158062770585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.887 × 10⁹⁸(99-digit number)

28875005012912658127…93312158062770585601

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

5.775 × 10⁹⁸(99-digit number)

57750010025825316255…86624316125541171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.775 × 10⁹⁸(99-digit number)

57750010025825316255…86624316125541171201

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

1.155 × 10⁹⁹(100-digit number)

11550002005165063251…73248632251082342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.155 × 10⁹⁹(100-digit number)

11550002005165063251…73248632251082342401

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

2.310 × 10⁹⁹(100-digit number)

23100004010330126502…46497264502164684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.310 × 10⁹⁹(100-digit number)

23100004010330126502…46497264502164684801

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 #2,054,335

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