Block #183,448

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 12:46:29 AM · Difficulty 9.8578 · 6,643,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33ce6e3ccdcf310ad3c3fece8f192809f56610024f35fcd6249d0ab266f123d4

View on Chainz ↗

Height

#183,448

Difficulty

9.857823

Transactions

Size

653 B

Version

Bits

09db9a50

Nonce

339,785

Timestamp

9/28/2013, 12:46:29 AM

Confirmations

6,643,315

Mined by

⛏️ P2SHAZiTmnNf8rLGh57dXLaDvym1r7qXMH63xh

Merkle Root

8a90c39e4e68496116503917ce13d9e716efe6bae40ecdeea314d0407ce0c5bd

Transactions (3)

Coinbase5d46d2081ea31f…71779a7e9a1e6e

1 in → 1 out10.3000 XPM109 B

AZiTmnNf…qXMH63xh

0e5999a48a336c…1bb4a024ba1a06

1 in → 2 out5.4699 XPM227 B

AWUfqb35…otT3cVBM AcXS3b8w…dKuXqTVX

a18227692a359f…e7fb6e467abb69

1 in → 2 out1.1491 XPM226 B

AMFYS3Um…pLt2LVAF AQ5egZqg…B8igkNQA

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.

8.309 × 10⁹⁶(97-digit number)

83091148058352739789…95722790480573369599

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

8.309 × 10⁹⁶(97-digit number)

83091148058352739789…95722790480573369599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.309 × 10⁹⁶(97-digit number)

83091148058352739789…95722790480573369601

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

1.661 × 10⁹⁷(98-digit number)

16618229611670547957…91445580961146739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.661 × 10⁹⁷(98-digit number)

16618229611670547957…91445580961146739201

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

3.323 × 10⁹⁷(98-digit number)

33236459223341095915…82891161922293478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.323 × 10⁹⁷(98-digit number)

33236459223341095915…82891161922293478401

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

6.647 × 10⁹⁷(98-digit number)

66472918446682191831…65782323844586956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.647 × 10⁹⁷(98-digit number)

66472918446682191831…65782323844586956801

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

1.329 × 10⁹⁸(99-digit number)

13294583689336438366…31564647689173913599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #183,448

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