Block #2,094,826

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2017, 9:20:02 PM · Difficulty 10.8719 · 4,745,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c6901523f3d5d71edec8d56a18116837be1ac5ad4d1067ab8f55429251547c0

View on Chainz ↗

Height

#2,094,826

Difficulty

10.871941

Transactions

Size

2.05 KB

Version

Bits

0adf3789

Nonce

1,443,303,182

Timestamp

4/30/2017, 9:20:02 PM

Confirmations

4,745,439

Mined by

⛏️ P2SHAWCi3xdxY3g53QwsTvz6kyiGHPnkSx9191

Merkle Root

35ddb63cf4b03345664ee54fa75a56a1a96b35512bd8bb5d2b3cbad8f2ff0a8f

Transactions (3)

Coinbase97dc49ded2de50…3dddfefd92fe0d

1 in → 1 out8.4800 XPM109 B

AWCi3xdx…nkSx9191

e4bcba9dabcfaf…fcf8b83145eb3e

11 in → 1 out7513.8847 XPM1.63 KB

Ada1dx2w…8gd1gZg2

a28bb893e721ee…77cf353a85f976

1 in → 2 out2.1271 XPM226 B

AeJxFmGJ…yDjFvNta AeYZTP6b…v53Q54vJ

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.

8.944 × 10⁹⁷(98-digit number)

89444527198793318324…26796863700743823359

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

8.944 × 10⁹⁷(98-digit number)

89444527198793318324…26796863700743823359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.944 × 10⁹⁷(98-digit number)

89444527198793318324…26796863700743823361

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

1.788 × 10⁹⁸(99-digit number)

17888905439758663664…53593727401487646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.788 × 10⁹⁸(99-digit number)

17888905439758663664…53593727401487646721

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

3.577 × 10⁹⁸(99-digit number)

35777810879517327329…07187454802975293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.577 × 10⁹⁸(99-digit number)

35777810879517327329…07187454802975293441

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

7.155 × 10⁹⁸(99-digit number)

71555621759034654659…14374909605950586879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.155 × 10⁹⁸(99-digit number)

71555621759034654659…14374909605950586881

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

1.431 × 10⁹⁹(100-digit number)

14311124351806930931…28749819211901173759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.431 × 10⁹⁹(100-digit number)

14311124351806930931…28749819211901173761

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 #2,094,826

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