Block #727,691

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/18/2014, 3:33:17 PM · Difficulty 10.9627 · 6,088,274 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a5dc19f521b4ec26e507e9e754011ea032480e2a0266b3fe4590719e2348930

View on Chainz ↗

Height

#727,691

Difficulty

10.962699

Transactions

Size

11.52 KB

Version

Bits

0af67375

Nonce

794,925,332

Timestamp

9/18/2014, 3:33:17 PM

Confirmations

6,088,274

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8050ded3d7c65dbfafe3a37830d8914c8ae2426bf24b3ab55387e4aa6123dc67

Transactions (4)

Coinbase2fa2ed832bb7fd…c5953b0d1e1d14

1 in → 1 out8.6500 XPM116 B

ANSXnLY2…Sd25TjkD

9294d798efe2a7…68ecaecdfe790a

74 in → 2 out1000.0100 XPM10.73 KB

AQaCJsaU…MRLEgb1G AdvurNjz…j1oXi361

986ee543d1a20a…4c222e13fe6693

2 in → 2 out11.2048 XPM376 B

AHdkjDnS…SYJhF91Y AL3C9mvn…piDDq1XP

9b344db6ae5a3f…e7822ce2cbdc17

1 in → 2 out5.4926 XPM225 B

ATXoRbuk…F7EfBiS6 ARAAzsWX…SVgcc6gw

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.

1.645 × 10⁹⁸(99-digit number)

16459815459200113249…91199767734142463999

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

1.645 × 10⁹⁸(99-digit number)

16459815459200113249…91199767734142463999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.645 × 10⁹⁸(99-digit number)

16459815459200113249…91199767734142464001

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

3.291 × 10⁹⁸(99-digit number)

32919630918400226498…82399535468284927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.291 × 10⁹⁸(99-digit number)

32919630918400226498…82399535468284928001

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

6.583 × 10⁹⁸(99-digit number)

65839261836800452997…64799070936569855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.583 × 10⁹⁸(99-digit number)

65839261836800452997…64799070936569856001

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

1.316 × 10⁹⁹(100-digit number)

13167852367360090599…29598141873139711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.316 × 10⁹⁹(100-digit number)

13167852367360090599…29598141873139712001

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

2.633 × 10⁹⁹(100-digit number)

26335704734720181198…59196283746279423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.633 × 10⁹⁹(100-digit number)

26335704734720181198…59196283746279424001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.267 × 10⁹⁹(100-digit number)

52671409469440362397…18392567492558847999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #727,691

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