Block #1,109,157

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2015, 5:47:31 AM · Difficulty 10.8524 · 5,717,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d2e9be946fa0e2e9dffe4d701f54106e8604b280c3cfa98de1d47210657b09d

View on Chainz ↗

Height

#1,109,157

Difficulty

10.852414

Transactions

Size

66.89 KB

Version

Bits

0ada37cc

Nonce

401,067,746

Timestamp

6/16/2015, 5:47:31 AM

Confirmations

5,717,467

Mined by

⛏️ P2SHAPudznNTd4D92Ztrj2RG3K9BMEnUDwzi1u

Merkle Root

335f5485f9a19192ae3c9d831ea9e7ee8b5345cfa367f055430522bdc8c64c19

Transactions (2)

Coinbase4ca4eb6581c7c2…5f85fca148a0ee

1 in → 1 out9.1900 XPM110 B

APudznNT…nUDwzi1u

99b5a51d27e342…372d544018c69d

461 in → 2 out605.0274 XPM66.70 KB

AG7qNB8k…GzEsDDRd APKirZWi…NTdN7ZTc

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.

1.927 × 10⁹⁸(99-digit number)

19277400004341332200…69310675926937272319

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

1.927 × 10⁹⁸(99-digit number)

19277400004341332200…69310675926937272319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.927 × 10⁹⁸(99-digit number)

19277400004341332200…69310675926937272321

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

3.855 × 10⁹⁸(99-digit number)

38554800008682664400…38621351853874544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.855 × 10⁹⁸(99-digit number)

38554800008682664400…38621351853874544641

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

7.710 × 10⁹⁸(99-digit number)

77109600017365328800…77242703707749089279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.710 × 10⁹⁸(99-digit number)

77109600017365328800…77242703707749089281

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

1.542 × 10⁹⁹(100-digit number)

15421920003473065760…54485407415498178559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.542 × 10⁹⁹(100-digit number)

15421920003473065760…54485407415498178561

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

3.084 × 10⁹⁹(100-digit number)

30843840006946131520…08970814830996357119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.084 × 10⁹⁹(100-digit number)

30843840006946131520…08970814830996357121

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 #1,109,157

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