Block #1,106,144

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/15/2015, 7:43:35 AM · Difficulty 10.7935 · 5,706,169 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e7c0c1714c14f19264bfb93b05fba159ff01d57587138b8553b964088f6e602

View on Chainz ↗

Height

#1,106,144

Difficulty

10.793530

Transactions

Size

243 B

Version

Bits

0acb24ce

Nonce

50,723,302

Timestamp

6/15/2015, 7:43:35 AM

Confirmations

5,706,169

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

44b766503f41d7ea5cc8bbc419aff623732e7aefec19e8211ab65fa69c8a487e

Transactions (1)

Coinbase44b766503f41d7…b65fa69c8a487e

1 in → 2 out8.5700 XPM152 B

APGBorYS…QnZrTNSi ALPu3s2c…EJXLjVFh

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.

2.205 × 10⁹⁷(98-digit number)

22054952977718069349…73296778536136191999

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

2.205 × 10⁹⁷(98-digit number)

22054952977718069349…73296778536136191999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.205 × 10⁹⁷(98-digit number)

22054952977718069349…73296778536136192001

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

4.410 × 10⁹⁷(98-digit number)

44109905955436138698…46593557072272383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.410 × 10⁹⁷(98-digit number)

44109905955436138698…46593557072272384001

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

8.821 × 10⁹⁷(98-digit number)

88219811910872277397…93187114144544767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.821 × 10⁹⁷(98-digit number)

88219811910872277397…93187114144544768001

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

1.764 × 10⁹⁸(99-digit number)

17643962382174455479…86374228289089535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.764 × 10⁹⁸(99-digit number)

17643962382174455479…86374228289089536001

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

3.528 × 10⁹⁸(99-digit number)

35287924764348910959…72748456578179071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.528 × 10⁹⁸(99-digit number)

35287924764348910959…72748456578179072001

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 #1,106,144

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