Block #2,093,694

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2017, 2:57:10 AM · Difficulty 10.8711 · 4,718,617 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e77691897b3e98458a6ff6372bfaba68d651ce09b0eae4e0606b3554ad04acf9

View on Chainz ↗

Height

#2,093,694

Difficulty

10.871106

Transactions

Size

732 B

Version

Bits

0adf00ce

Nonce

182,302,058

Timestamp

4/30/2017, 2:57:10 AM

Confirmations

4,718,617

Mined by

⛏️ P2SHAWW13vPBzG8xTErbzXzx64xiz4YESTjUi3

Merkle Root

b9c997d06943f08eda6e8b808f852e63177b0eba577cdbee5185e828b673749c

Transactions (2)

Coinbasedfe8be015ec3d3…d749cfffb4c8a8

1 in → 1 out8.4600 XPM110 B

AWW13vPB…YESTjUi3

a840e211c0b4df…08058a5356cf9b

1 in → 11 out4.3360 XPM531 B

AFxxYVtW…76zFbjN1 AV54jZRU…XWwhnVCg AM9MGsvG…w6mcBFi1 AUiLptzJ…dTU4Jj5R AcNVQYAc…RUWKwCFu

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.

1.022 × 10⁹⁷(98-digit number)

10223534114314289756…04921782608712990719

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

1.022 × 10⁹⁷(98-digit number)

10223534114314289756…04921782608712990719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.022 × 10⁹⁷(98-digit number)

10223534114314289756…04921782608712990721

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

2.044 × 10⁹⁷(98-digit number)

20447068228628579513…09843565217425981439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.044 × 10⁹⁷(98-digit number)

20447068228628579513…09843565217425981441

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

4.089 × 10⁹⁷(98-digit number)

40894136457257159027…19687130434851962879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.089 × 10⁹⁷(98-digit number)

40894136457257159027…19687130434851962881

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

8.178 × 10⁹⁷(98-digit number)

81788272914514318055…39374260869703925759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.178 × 10⁹⁷(98-digit number)

81788272914514318055…39374260869703925761

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

1.635 × 10⁹⁸(99-digit number)

16357654582902863611…78748521739407851519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.635 × 10⁹⁸(99-digit number)

16357654582902863611…78748521739407851521

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 #2,093,694

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