Block #489,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 10:04:39 AM · Difficulty 10.6671 · 6,337,521 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b31ec169f7cf1b0aa8c9116b45041c5e3c248f8fd22e08d679e0615f9a27b36a

View on Chainz ↗

Height

#489,636

Difficulty

10.667132

Transactions

Size

1.22 KB

Version

Bits

0aaac92a

Nonce

55,021,829

Timestamp

4/13/2014, 10:04:39 AM

Confirmations

6,337,521

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4bc86e3084d57661ba973aa6318e90e763a7cc655ac2d26bcf2235432a9f212b

Transactions (3)

Coinbase280439faede2e6…952d1a21038179

1 in → 1 out8.7900 XPM116 B

AbwWkWZt…kawDhufa

c55495feef2322…08ed670a488075

2 in → 2 out2.5746 XPM375 B

AMFPg3WV…Z4WxWJSX AYy6jDKp…aS5b1Ft6

95bc600bda6260…618e9ab687b003

4 in → 2 out2.5107 XPM668 B

ATWqKJZL…RU8T56Ff AUyH1wu5…VX9sVQq5

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.

1.099 × 10⁹⁹(100-digit number)

10998917878417606580…92274419255158154879

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

1.099 × 10⁹⁹(100-digit number)

10998917878417606580…92274419255158154879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.099 × 10⁹⁹(100-digit number)

10998917878417606580…92274419255158154881

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

2.199 × 10⁹⁹(100-digit number)

21997835756835213161…84548838510316309759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.199 × 10⁹⁹(100-digit number)

21997835756835213161…84548838510316309761

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

4.399 × 10⁹⁹(100-digit number)

43995671513670426323…69097677020632619519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.399 × 10⁹⁹(100-digit number)

43995671513670426323…69097677020632619521

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

8.799 × 10⁹⁹(100-digit number)

87991343027340852647…38195354041265239039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.799 × 10⁹⁹(100-digit number)

87991343027340852647…38195354041265239041

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

1.759 × 10¹⁰⁰(101-digit number)

17598268605468170529…76390708082530478079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.759 × 10¹⁰⁰(101-digit number)

17598268605468170529…76390708082530478081

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #489,636

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