Block #88,353

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 1:55:51 PM · Difficulty 9.2678 · 6,737,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6580b85018349ca253086a8023e30833e29b50f8c8e2c1e1eaf73c081536a66

View on Chainz ↗

Height

#88,353

Difficulty

9.267780

Transactions

Size

1.45 KB

Version

Bits

09448d3a

Nonce

29,087

Timestamp

7/29/2013, 1:55:51 PM

Confirmations

6,737,221

Mined by

⛏️ P2SHAcroMthgEmywp9em9N8omLrXsUzxLfFxZj

Merkle Root

d426c71b1de42023f3af4002463909927f27c4841199f0289e04d3f98024887c

Transactions (4)

Coinbase0d27ad64d0eaee…5a93d40e0060fd

1 in → 1 out11.6600 XPM109 B

AcroMthg…zxLfFxZj

475833cace3ebd…b5fc293be15603

6 in → 2 out109.9183 XPM965 B

AWBeDGaB…GaKKiPyH AbVr8xUr…PrqbB6tp

92f3060eb0e016…be87fa2efca315

1 in → 1 out11.6200 XPM159 B

AbQVuXmJ…qZjmTccE

fcecdd91ec3eec…135538bfe60beb

1 in → 1 out11.5800 XPM159 B

AJjQKwJb…3qe2NN54

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.

4.095 × 10¹¹⁰(111-digit number)

40951146685111539044…89077154642121829219

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

4.095 × 10¹¹⁰(111-digit number)

40951146685111539044…89077154642121829219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.095 × 10¹¹⁰(111-digit number)

40951146685111539044…89077154642121829221

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

8.190 × 10¹¹⁰(111-digit number)

81902293370223078089…78154309284243658439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.190 × 10¹¹⁰(111-digit number)

81902293370223078089…78154309284243658441

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

1.638 × 10¹¹¹(112-digit number)

16380458674044615617…56308618568487316879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.638 × 10¹¹¹(112-digit number)

16380458674044615617…56308618568487316881

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

3.276 × 10¹¹¹(112-digit number)

32760917348089231235…12617237136974633759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.276 × 10¹¹¹(112-digit number)

32760917348089231235…12617237136974633761

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

6.552 × 10¹¹¹(112-digit number)

65521834696178462471…25234474273949267519

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 #88,353

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