Block #792,802

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/1/2014, 10:05:38 PM · Difficulty 10.9739 · 6,016,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

493f7ccc2c91bfca4f031bc2f8d8566eba3fd5f1a5f74e1ab8ea04d4e8c0c433

View on Chainz ↗

Height

#792,802

Difficulty

10.973854

Transactions

Size

1.09 KB

Version

Bits

0af94e7f

Nonce

153,348,189

Timestamp

11/1/2014, 10:05:38 PM

Confirmations

6,016,651

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1a8a47c9181a715669c814e47fe4edd98796afd42d42c9c5e97d53542bf5c4ae

Transactions (5)

Coinbase02fc3ef2aac75e…a3c3c7018c46dd

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

95cf603a24c89b…bf85af3b137a36

1 in → 2 out6.7582 XPM226 B

AREmLC5L…3hsWg33i AGCEDJwd…rQ6kXYEP

8ab50342409911…b4fb596aa52af9

1 in → 2 out7.4418 XPM226 B

AdUcK4uN…U9vSn1DL AGdWVjRk…LFVsqCnK

cca6ac02ad2940…712d510a9ce0e4

1 in → 2 out7.2498 XPM227 B

AL8qoC7j…hHpiSCoG APaYVt8e…rPF99zd2

0fac835f59e470…6a10fac3d61a67

1 in → 2 out4.3330 XPM227 B

AZFCszA5…YEbKqMZo AMKe4rZR…N35e14r8

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.

4.112 × 10⁹⁹(100-digit number)

41120388630901184593…83291049474746777599

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

4.112 × 10⁹⁹(100-digit number)

41120388630901184593…83291049474746777599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.112 × 10⁹⁹(100-digit number)

41120388630901184593…83291049474746777601

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

8.224 × 10⁹⁹(100-digit number)

82240777261802369186…66582098949493555199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.224 × 10⁹⁹(100-digit number)

82240777261802369186…66582098949493555201

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

1.644 × 10¹⁰⁰(101-digit number)

16448155452360473837…33164197898987110399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.644 × 10¹⁰⁰(101-digit number)

16448155452360473837…33164197898987110401

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

3.289 × 10¹⁰⁰(101-digit number)

32896310904720947674…66328395797974220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.289 × 10¹⁰⁰(101-digit number)

32896310904720947674…66328395797974220801

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

6.579 × 10¹⁰⁰(101-digit number)

65792621809441895349…32656791595948441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.579 × 10¹⁰⁰(101-digit number)

65792621809441895349…32656791595948441601

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

1.315 × 10¹⁰¹(102-digit number)

13158524361888379069…65313583191896883199

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 #792,802

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