Block #2,142,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/3/2017, 4:41:02 AM · Difficulty 10.8784 · 4,700,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48913d7f9bcd4d09596f389c481391d189490322668a4932c72b8496564a9962

View on Chainz ↗

Height

#2,142,976

Difficulty

10.878423

Transactions

Size

878 B

Version

Bits

0ae0e059

Nonce

330,419,979

Timestamp

6/3/2017, 4:41:02 AM

Confirmations

4,700,071

Mined by

⛏️ P2SHALVJQi1vF46iA5JqVuCYoMvVg1z9gAHt6J

Merkle Root

35433edd33edec952360e763346fd7f2ef12a99d8b247cc857b31c56671ad2ca

Transactions (4)

Coinbase3908b476348641…ffd1aa40c469bf

1 in → 1 out8.4700 XPM109 B

ALVJQi1v…z9gAHt6J

df17857d34494f…88cfc2f40ffa4b

1 in → 2 out176819.0940 XPM226 B

ANysiTDC…eHu8LCaU AQV8RafG…4QyJ6sZf

29dfc2dc3e2b18…42e24e9aca29e5

1 in → 2 out175051.9167 XPM226 B

AHzw9T1D…Jjs1SNo1 AV2FALkZ…xwSeEKGK

c6e7354dd890ed…71d9055a896e94

1 in → 2 out174208.5777 XPM225 B

Aah2d57o…2KitT5d6 AK2bipW8…cgbaenXu

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.

3.896 × 10⁹⁸(99-digit number)

38968946649529774607…65852792976162488319

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

3.896 × 10⁹⁸(99-digit number)

38968946649529774607…65852792976162488319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.896 × 10⁹⁸(99-digit number)

38968946649529774607…65852792976162488321

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

7.793 × 10⁹⁸(99-digit number)

77937893299059549215…31705585952324976639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.793 × 10⁹⁸(99-digit number)

77937893299059549215…31705585952324976641

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

1.558 × 10⁹⁹(100-digit number)

15587578659811909843…63411171904649953279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.558 × 10⁹⁹(100-digit number)

15587578659811909843…63411171904649953281

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

3.117 × 10⁹⁹(100-digit number)

31175157319623819686…26822343809299906559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.117 × 10⁹⁹(100-digit number)

31175157319623819686…26822343809299906561

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

6.235 × 10⁹⁹(100-digit number)

62350314639247639372…53644687618599813119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.235 × 10⁹⁹(100-digit number)

62350314639247639372…53644687618599813121

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 #2,142,976

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