Block #1,097,750

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/10/2015, 1:39:20 AM · Difficulty 10.7563 · 5,719,460 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bbdd73c991f6510632d0d10c423843c41b97f8a6af289c7ce5560752630811e

View on Chainz ↗

Height

#1,097,750

Difficulty

10.756309

Transactions

Size

2.23 KB

Version

Bits

0ac19d7d

Nonce

1,906,502,166

Timestamp

6/10/2015, 1:39:20 AM

Confirmations

5,719,460

Mined by

⛏️ P2SHAV4yz34jL7h6Q91PqxTBhtCJNKXCLgMyAJ

Merkle Root

a08429421a637b207525728cae722b0b34814fddfd2af032e79e1a091bfb9703

Transactions (3)

Coinbaseecc21bded7bc78…6db23685c34e60

1 in → 1 out8.6600 XPM109 B

AV4yz34j…XCLgMyAJ

9d3433dd7b819c…c56b3ac1736236

12 in → 2 out103.2295 XPM1.81 KB

AXhsX5xX…q2ccbLP5 AYft9KNE…3h2Kzybn

940acc693ff2b9…a13575f347d2dd

1 in → 2 out8.6400 XPM226 B

AeBwvm57…kL6E7ayF AarjPs54…sV1bH6UD

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.

5.664 × 10⁹⁸(99-digit number)

56649890907389840364…13970165439687065599

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

5.664 × 10⁹⁸(99-digit number)

56649890907389840364…13970165439687065599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.664 × 10⁹⁸(99-digit number)

56649890907389840364…13970165439687065601

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

1.132 × 10⁹⁹(100-digit number)

11329978181477968072…27940330879374131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.132 × 10⁹⁹(100-digit number)

11329978181477968072…27940330879374131201

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

2.265 × 10⁹⁹(100-digit number)

22659956362955936145…55880661758748262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.265 × 10⁹⁹(100-digit number)

22659956362955936145…55880661758748262401

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

4.531 × 10⁹⁹(100-digit number)

45319912725911872291…11761323517496524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.531 × 10⁹⁹(100-digit number)

45319912725911872291…11761323517496524801

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

9.063 × 10⁹⁹(100-digit number)

90639825451823744582…23522647034993049599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.063 × 10⁹⁹(100-digit number)

90639825451823744582…23522647034993049601

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 #1,097,750

Cookie Preferences