Block #82,911

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 6:29:55 PM · Difficulty 9.2733 · 6,741,855 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5dadc09775b7b4c2d70f1c198e97e501a8809f094249c9e595c4ee0668f23501

View on Chainz ↗

Height

#82,911

Difficulty

9.273292

Transactions

Size

523 B

Version

Bits

0945f67e

Nonce

1,257

Timestamp

7/25/2013, 6:29:55 PM

Confirmations

6,741,855

Mined by

⛏️ P2SHAYKees98nFSmfsQcZpkYDr7VSmc2Su2fbZ

Merkle Root

eb78eaf1f56224ff1e50b00e8f637b8ebd593018fd781841be1a54fdc5c3b962

Transactions (3)

Coinbasec93aecdffc2e50…937b1a1e140cc2

1 in → 1 out11.6300 XPM110 B

AYKees98…c2Su2fbZ

00f2b89fb90375…0abe2badde0fdc

1 in → 1 out12.3400 XPM157 B

AQ7ecuQu…G8JZu6qc

2eba6242d29e9c…a679551c617054

1 in → 1 out11.6700 XPM158 B

ASj7fWPU…by8b9uAs

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.

1.239 × 10¹¹⁵(116-digit number)

12397035276500628896…99765961936437271289

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

1.239 × 10¹¹⁵(116-digit number)

12397035276500628896…99765961936437271289

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.239 × 10¹¹⁵(116-digit number)

12397035276500628896…99765961936437271291

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

2.479 × 10¹¹⁵(116-digit number)

24794070553001257793…99531923872874542579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.479 × 10¹¹⁵(116-digit number)

24794070553001257793…99531923872874542581

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

4.958 × 10¹¹⁵(116-digit number)

49588141106002515586…99063847745749085159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.958 × 10¹¹⁵(116-digit number)

49588141106002515586…99063847745749085161

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

9.917 × 10¹¹⁵(116-digit number)

99176282212005031172…98127695491498170319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.917 × 10¹¹⁵(116-digit number)

99176282212005031172…98127695491498170321

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

1.983 × 10¹¹⁶(117-digit number)

19835256442401006234…96255390982996340639

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 #82,911

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