Block #283,944

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 10:46:31 PM · Difficulty 9.9819 · 6,522,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6a88ba2f4a5bf848c58d2c015d9f77592a01fbe4344852c1aa8fddae23cb14f

View on Chainz ↗

Height

#283,944

Difficulty

9.981903

Transactions

Size

1.85 KB

Version

Bits

09fb5e05

Nonce

9,179

Timestamp

11/29/2013, 10:46:31 PM

Confirmations

6,522,348

Mined by

⛏️ UaR^AHseojs399duLLZKw9KkmE61Rn6sv2MoE1

Merkle Root

2079cb6747d71566fef1bf6a84f9b9f19defdb9740860055965153872b18bd55

Transactions (4)

Coinbase62264ff2b77b35…7f0627b0915f30

1 in → 28 out10.0000 XPM1015 B

AHseojs3…6sv2MoE1 AQwRN8bE…V8PsTcY9 AcC2zSod…rtWatH79 AJHH6QuE…N3s6fxLC AP35e64F…amMs1Qnk

b059eee1910331…fb206db071e332

2 in → 1 out10.7080 XPM340 B

AciRLg1W…p6n9PmXA

864606c8eb4813…90319f25f31e87

1 in → 2 out5.4254 XPM226 B

AP7dz8cU…bUkG44oS AZtFPifF…DaugVair

073edef5185b3d…3bdc1b4bb82040

1 in → 2 out4.6475 XPM226 B

AGQxR1oS…2N1xAZXN ATgYucze…f9k56zzw

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.

2.210 × 10⁹⁷(98-digit number)

22107901802694672510…37471828435027046399

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

2.210 × 10⁹⁷(98-digit number)

22107901802694672510…37471828435027046399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.210 × 10⁹⁷(98-digit number)

22107901802694672510…37471828435027046401

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

4.421 × 10⁹⁷(98-digit number)

44215803605389345020…74943656870054092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.421 × 10⁹⁷(98-digit number)

44215803605389345020…74943656870054092801

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

8.843 × 10⁹⁷(98-digit number)

88431607210778690041…49887313740108185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.843 × 10⁹⁷(98-digit number)

88431607210778690041…49887313740108185601

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

1.768 × 10⁹⁸(99-digit number)

17686321442155738008…99774627480216371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.768 × 10⁹⁸(99-digit number)

17686321442155738008…99774627480216371201

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

3.537 × 10⁹⁸(99-digit number)

35372642884311476016…99549254960432742399

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 #283,944

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