Block #489,714

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/13/2014, 11:17:27 AM · Difficulty 10.6677 · 6,337,172 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14286bb950ae010386b655be5cedcfced9076e3d345fabcd0e24fd55d413dae1

View on Chainz ↗

Height

#489,714

Difficulty

10.667742

Transactions

Size

832 B

Version

Bits

0aaaf11d

Nonce

517,361

Timestamp

4/13/2014, 11:17:27 AM

Confirmations

6,337,172

Mined by

⛏️ xaSJqrgAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e6846c8472033cbd13f984cef904fca978a8ee8c32a89a17dcd9cc5b328be5cc

Transactions (1)

Coinbasee6846c8472033c…d9cc5b328be5cc

1 in → 20 out8.7693 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

5.452 × 10⁹¹(92-digit number)

54529127944838576186…81075125941632126679

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

5.452 × 10⁹¹(92-digit number)

54529127944838576186…81075125941632126679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.452 × 10⁹¹(92-digit number)

54529127944838576186…81075125941632126681

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

1.090 × 10⁹²(93-digit number)

10905825588967715237…62150251883264253359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.090 × 10⁹²(93-digit number)

10905825588967715237…62150251883264253361

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

2.181 × 10⁹²(93-digit number)

21811651177935430474…24300503766528506719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.181 × 10⁹²(93-digit number)

21811651177935430474…24300503766528506721

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

4.362 × 10⁹²(93-digit number)

43623302355870860949…48601007533057013439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.362 × 10⁹²(93-digit number)

43623302355870860949…48601007533057013441

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

8.724 × 10⁹²(93-digit number)

87246604711741721898…97202015066114026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.724 × 10⁹²(93-digit number)

87246604711741721898…97202015066114026881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.744 × 10⁹³(94-digit number)

17449320942348344379…94404030132228053759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #489,714

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