Block #88,833

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 10:01:56 PM · Difficulty 9.2665 · 6,703,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7daf72b1a34ad4432b5305194ff0238ef26dbba0b7d09f0b9c1469db3c00f52

View on Chainz ↗

Height

#88,833

Difficulty

9.266548

Transactions

Size

4.21 KB

Version

Bits

09443c78

Nonce

136,763

Timestamp

7/29/2013, 10:01:56 PM

Confirmations

6,703,629

Merkle Root

470941cbd6b389d7a3e09e1368860c2f111541572c867dde722626e39bd6c8a4

Transactions (2)

Coinbasec22d4367386b28…84106fa36a6ecf

1 in → 1 out11.6800 XPM109 B

AXFoMTET…jr1Vcy4w

a4ea8392fb1031…bcb25b4e887fc0

35 in → 3 out405.2600 XPM4.00 KB

AGfz3APU…kNJNtgfb AQ9VkUy6…TuxTAEug AcX1kdjQ…Smx1H1dd

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.

3.983 × 10¹¹⁰(111-digit number)

39834384159715276109…02418514582761443199

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

3.983 × 10¹¹⁰(111-digit number)

39834384159715276109…02418514582761443199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.983 × 10¹¹⁰(111-digit number)

39834384159715276109…02418514582761443201

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

7.966 × 10¹¹⁰(111-digit number)

79668768319430552219…04837029165522886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.966 × 10¹¹⁰(111-digit number)

79668768319430552219…04837029165522886401

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

1.593 × 10¹¹¹(112-digit number)

15933753663886110443…09674058331045772799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.593 × 10¹¹¹(112-digit number)

15933753663886110443…09674058331045772801

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

3.186 × 10¹¹¹(112-digit number)

31867507327772220887…19348116662091545599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.186 × 10¹¹¹(112-digit number)

31867507327772220887…19348116662091545601

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

6.373 × 10¹¹¹(112-digit number)

63735014655544441775…38696233324183091199

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