Block #2,074,482

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2017, 1:48:29 PM · Difficulty 10.8376 · 4,758,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f21df92093e658874b11cfeb031a10c0f71da496b48f68e90bcd661bf7035e1

View on Chainz ↗

Height

#2,074,482

Difficulty

10.837604

Transactions

Size

870 B

Version

Bits

0ad66d33

Nonce

491,908,002

Timestamp

4/17/2017, 1:48:29 PM

Confirmations

4,758,046

Mined by

⛏️ P2SHALKt33CRGhLCWXqBf94SBEDhV79rEVJYLM

Merkle Root

540182a1e30950c7cbd54224781e0377964b5c7d3cdb0f24ea2a4eea7fe9d042

Transactions (2)

Coinbase3bf7c5c81c6127…6ec6b75d5b4bd7

1 in → 1 out8.5200 XPM109 B

ALKt33CR…9rEVJYLM

27c16d4e316bd8…4a20b713ea3db9

4 in → 2 out3661.1880 XPM670 B

AYoy228q…feZqXfNq AJXpsYVy…ZPLNiqiy

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.

1.198 × 10⁹⁶(97-digit number)

11988983882890350887…07066634426885565439

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

1.198 × 10⁹⁶(97-digit number)

11988983882890350887…07066634426885565439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.198 × 10⁹⁶(97-digit number)

11988983882890350887…07066634426885565441

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

2.397 × 10⁹⁶(97-digit number)

23977967765780701774…14133268853771130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.397 × 10⁹⁶(97-digit number)

23977967765780701774…14133268853771130881

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

4.795 × 10⁹⁶(97-digit number)

47955935531561403549…28266537707542261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.795 × 10⁹⁶(97-digit number)

47955935531561403549…28266537707542261761

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

9.591 × 10⁹⁶(97-digit number)

95911871063122807098…56533075415084523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.591 × 10⁹⁶(97-digit number)

95911871063122807098…56533075415084523521

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

1.918 × 10⁹⁷(98-digit number)

19182374212624561419…13066150830169047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.918 × 10⁹⁷(98-digit number)

19182374212624561419…13066150830169047041

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 #2,074,482

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