Block #283,164

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 3:35:15 PM · Difficulty 9.9806 · 6,512,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

155425f9074b9ad0c7c4c173a0728b5ccf9647e3cf8f225948a1b5d48872debb

View on Chainz ↗

Height

#283,164

Difficulty

9.980583

Transactions

Size

5.07 KB

Version

Bits

09fb0785

Nonce

8,074

Timestamp

11/29/2013, 3:35:15 PM

Confirmations

6,512,668

Mined by

⛏️ P2SHATosJnAckN3bgQY58u7jKurMx7UzfRgXp8

Merkle Root

63dae0d2fcd9a93b6acd15144c3bb0fd8b650e36c57ab7fdffd041b79521d4a7

Transactions (4)

Coinbase97876d2a420a6b…7ed6a5efab5c47

1 in → 1 out10.0900 XPM109 B

ATosJnAc…UzfRgXp8

93131a8289d53d…06f2333696f27a

5 in → 13 out50.2600 XPM1022 B

AVdWpPFc…EBRQUE9w AGN47MX3…rXJKHoga AGL4LiqG…EV8dqG2J AWWm6bsN…mbTWFe7X AUSzWVwW…b7pHWLbB

d79f143779ceaa…de26650a116364

25 in → 2 out8.1481 XPM3.69 KB

AH6qpoof…b68oxFrj ARUc32q2…KpHvkV9Y

6327c79de71727…1a83a58a4955d7

1 in → 1 out0.0900 XPM192 B

ANV6D3KX…Lnjn3pZX

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.

2.432 × 10⁹⁸(99-digit number)

24325902891363962598…61078806677190091199

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

2.432 × 10⁹⁸(99-digit number)

24325902891363962598…61078806677190091199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.432 × 10⁹⁸(99-digit number)

24325902891363962598…61078806677190091201

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

4.865 × 10⁹⁸(99-digit number)

48651805782727925197…22157613354380182399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.865 × 10⁹⁸(99-digit number)

48651805782727925197…22157613354380182401

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

9.730 × 10⁹⁸(99-digit number)

97303611565455850394…44315226708760364799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.730 × 10⁹⁸(99-digit number)

97303611565455850394…44315226708760364801

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

1.946 × 10⁹⁹(100-digit number)

19460722313091170078…88630453417520729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.946 × 10⁹⁹(100-digit number)

19460722313091170078…88630453417520729601

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

3.892 × 10⁹⁹(100-digit number)

38921444626182340157…77260906835041459199

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