Block #2,170,790

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2017, 5:22:19 PM · Difficulty 10.9037 · 4,667,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e290374a5a1ee7f1c354adcfcb08770c5c3a765ff0aa6d2c4c96498337a80c97

View on Chainz ↗

Height

#2,170,790

Difficulty

10.903721

Transactions

Size

723 B

Version

Bits

0ae75a46

Nonce

28,688,212

Timestamp

6/21/2017, 5:22:19 PM

Confirmations

4,667,728

Mined by

⛏️ P2SHAMiYXHihUMrHCpRAHb3HBRunPFDPKNhcdm

Merkle Root

22dffb24d2806710348a49f457723866670a60018dd10d56625fd5449755f61c

Transactions (2)

Coinbaseb53d96b07573b0…4f08e1bca94292

1 in → 1 out8.4100 XPM110 B

AMiYXHih…DPKNhcdm

054271d3cf8dc8…ed5c920e88d796

3 in → 2 out2916.0624 XPM522 B

AQZVhvkQ…55MyFfM2 ALHZ4BEJ…y67m6224

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.

2.598 × 10⁹⁷(98-digit number)

25984354634802888023…37212354340450565119

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

2.598 × 10⁹⁷(98-digit number)

25984354634802888023…37212354340450565119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.598 × 10⁹⁷(98-digit number)

25984354634802888023…37212354340450565121

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

5.196 × 10⁹⁷(98-digit number)

51968709269605776047…74424708680901130239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.196 × 10⁹⁷(98-digit number)

51968709269605776047…74424708680901130241

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

1.039 × 10⁹⁸(99-digit number)

10393741853921155209…48849417361802260479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.039 × 10⁹⁸(99-digit number)

10393741853921155209…48849417361802260481

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

2.078 × 10⁹⁸(99-digit number)

20787483707842310419…97698834723604520959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.078 × 10⁹⁸(99-digit number)

20787483707842310419…97698834723604520961

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

4.157 × 10⁹⁸(99-digit number)

41574967415684620838…95397669447209041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.157 × 10⁹⁸(99-digit number)

41574967415684620838…95397669447209041921

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 #2,170,790

Cookie Preferences