Block #88,763

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 9:07:57 PM · Difficulty 9.2645 · 6,719,695 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1cc02c85485abf4bf3c76d00036c0a3b173ea4b2e059ea9e72729625891d2d66

View on Chainz ↗

Height

#88,763

Difficulty

9.264478

Transactions

Size

1.28 KB

Version

Bits

0943b4d7

Nonce

126,533

Timestamp

7/29/2013, 9:07:57 PM

Confirmations

6,719,695

Mined by

⛏️ P2SHAP26k64HW986tKWaz26yPEYsqi34yG9qNM

Merkle Root

300d7b98a83f3bd109dd6a2372df566047a417aa09c16d1c91eef6d45a9c7a9f

Transactions (3)

Coinbase42015e6e6e9904…e26dcdbf072dba

1 in → 1 out11.6500 XPM109 B

AP26k64H…34yG9qNM

fe3e981713482f…4621ec4660a285

7 in → 2 out84.1511 XPM876 B

AecLmW7x…hiEBvF7u AS7fsUAi…yVWQoB2T

9c8026d76c4526…6a36e6016919e4

1 in → 2 out1.2096 XPM225 B

ATydKKqM…tGFJkM9S ARx4bG4A…CdNNNXiy

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.

1.416 × 10¹¹¹(112-digit number)

14167152314260442235…96535437707849190949

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

1.416 × 10¹¹¹(112-digit number)

14167152314260442235…96535437707849190949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.416 × 10¹¹¹(112-digit number)

14167152314260442235…96535437707849190951

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

2.833 × 10¹¹¹(112-digit number)

28334304628520884471…93070875415698381899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.833 × 10¹¹¹(112-digit number)

28334304628520884471…93070875415698381901

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

5.666 × 10¹¹¹(112-digit number)

56668609257041768942…86141750831396763799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.666 × 10¹¹¹(112-digit number)

56668609257041768942…86141750831396763801

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

1.133 × 10¹¹²(113-digit number)

11333721851408353788…72283501662793527599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.133 × 10¹¹²(113-digit number)

11333721851408353788…72283501662793527601

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

2.266 × 10¹¹²(113-digit number)

22667443702816707577…44567003325587055199

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 #88,763

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