Block #2,144,045

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/3/2017, 7:07:39 PM · Difficulty 10.8832 · 4,687,235 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dae160856a19e2a834385ac82e27067771fdee9d0f5428aee035e4682c0b16f8

View on Chainz ↗

Height

#2,144,045

Difficulty

10.883239

Transactions

Size

427 B

Version

Bits

0ae21bf8

Nonce

1,204,837,823

Timestamp

6/3/2017, 7:07:39 PM

Confirmations

4,687,235

Mined by

⛏️ P2SHAeApiK1jgK8ZpKqaRXCnmKgxubAimAeGo3

Merkle Root

924722d617da6e14e4f3377e24dfe37c114323b4877a960da01e6101bbe2a9c4

Transactions (2)

Coinbasef283e2faf85eb0…7863ed03b06277

1 in → 1 out8.4400 XPM109 B

AeApiK1j…AimAeGo3

f0164d454ac214…a1868bfc8eb5f8

1 in → 2 out173182.1087 XPM227 B

ATNNwPCV…id21vw5x ANyCWjQE…p9rSM1JK

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.

9.504 × 10⁹⁷(98-digit number)

95044694723124100236…90123227892923105279

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

9.504 × 10⁹⁷(98-digit number)

95044694723124100236…90123227892923105279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.504 × 10⁹⁷(98-digit number)

95044694723124100236…90123227892923105281

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

1.900 × 10⁹⁸(99-digit number)

19008938944624820047…80246455785846210559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.900 × 10⁹⁸(99-digit number)

19008938944624820047…80246455785846210561

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

3.801 × 10⁹⁸(99-digit number)

38017877889249640094…60492911571692421119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.801 × 10⁹⁸(99-digit number)

38017877889249640094…60492911571692421121

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

7.603 × 10⁹⁸(99-digit number)

76035755778499280188…20985823143384842239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.603 × 10⁹⁸(99-digit number)

76035755778499280188…20985823143384842241

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

1.520 × 10⁹⁹(100-digit number)

15207151155699856037…41971646286769684479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.520 × 10⁹⁹(100-digit number)

15207151155699856037…41971646286769684481

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 #2,144,045

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