Block #1,184,226

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/6/2015, 3:44:46 AM · Difficulty 10.8993 · 5,655,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b3eac7a8fd1a953de51dd8066890c67dae71ce33948485003e9c9de1e5e426b

View on Chainz ↗

Height

#1,184,226

Difficulty

10.899347

Transactions

Size

4.46 KB

Version

Bits

0ae63b95

Nonce

128,844,093

Timestamp

8/6/2015, 3:44:46 AM

Confirmations

5,655,957

Mined by

⛏️ P2SHAPbBP2QTaAatLR98kijwZej12PScCL4pU9

Merkle Root

aca855b1ac20de19308e14c293205733a97f51b2cef9ba600b74607d5a138c6b

Transactions (2)

Coinbase1ff9a12c6afefa…1dc35357dea255

1 in → 1 out8.4500 XPM109 B

APbBP2QT…ScCL4pU9

35b891e0299d64…f971f538d9a116

29 in → 2 out105.3290 XPM4.26 KB

ARzmiMFq…xSMPipLn ARoPpPjC…Ndoa3iQv

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.

1.640 × 10⁹⁸(99-digit number)

16408404844020256929…34456002763569233919

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

1.640 × 10⁹⁸(99-digit number)

16408404844020256929…34456002763569233919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.640 × 10⁹⁸(99-digit number)

16408404844020256929…34456002763569233921

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

3.281 × 10⁹⁸(99-digit number)

32816809688040513859…68912005527138467839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.281 × 10⁹⁸(99-digit number)

32816809688040513859…68912005527138467841

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

6.563 × 10⁹⁸(99-digit number)

65633619376081027718…37824011054276935679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.563 × 10⁹⁸(99-digit number)

65633619376081027718…37824011054276935681

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

1.312 × 10⁹⁹(100-digit number)

13126723875216205543…75648022108553871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.312 × 10⁹⁹(100-digit number)

13126723875216205543…75648022108553871361

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

2.625 × 10⁹⁹(100-digit number)

26253447750432411087…51296044217107742719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.625 × 10⁹⁹(100-digit number)

26253447750432411087…51296044217107742721

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 #1,184,226

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