Block #832,815

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/29/2014, 5:54:30 AM · Difficulty 10.9782 · 5,976,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40d53b94c2059c9192b4ff21f3926a75da6da34f61031ed864566cd606a40c1c

View on Chainz ↗

Height

#832,815

Difficulty

10.978247

Transactions

Size

886 B

Version

Bits

0afa6e61

Nonce

2,812,413,913

Timestamp

11/29/2014, 5:54:30 AM

Confirmations

5,976,746

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

16f292f48dbc8d563040dee2a1503ba0215fee98c4a20e6e85cd44d18fd78e3d

Transactions (4)

Coinbase8c43eaf7ae6dc3…ef50c29ce0ab30

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

8491bc2863257d…31d980e58b4aa4

1 in → 2 out8.2700 XPM226 B

AWHiEceV…xz52viB8 AMuYYsgd…ioD1TEUt

533e5bf42cf3e0…720d6d607b0e7c

1 in → 2 out8.2700 XPM225 B

AS64CRJG…SESGw61o ALNQaD7f…2g74yYvV

3769cf7f1d8d97…454d8daeefcbc1

1 in → 2 out8.2700 XPM227 B

ARPTErkK…aFjTeuWm AccMQQ2K…qpURjHmC

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.

4.591 × 10⁹⁹(100-digit number)

45917913845359012935…76729779057500159999

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

4.591 × 10⁹⁹(100-digit number)

45917913845359012935…76729779057500159999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.591 × 10⁹⁹(100-digit number)

45917913845359012935…76729779057500160001

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

9.183 × 10⁹⁹(100-digit number)

91835827690718025870…53459558115000319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.183 × 10⁹⁹(100-digit number)

91835827690718025870…53459558115000320001

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

1.836 × 10¹⁰⁰(101-digit number)

18367165538143605174…06919116230000639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.836 × 10¹⁰⁰(101-digit number)

18367165538143605174…06919116230000640001

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

3.673 × 10¹⁰⁰(101-digit number)

36734331076287210348…13838232460001279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.673 × 10¹⁰⁰(101-digit number)

36734331076287210348…13838232460001280001

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

7.346 × 10¹⁰⁰(101-digit number)

73468662152574420696…27676464920002559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.346 × 10¹⁰⁰(101-digit number)

73468662152574420696…27676464920002560001

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

1.469 × 10¹⁰¹(102-digit number)

14693732430514884139…55352929840005119999

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 #832,815

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