Block #485,827

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 7:01:22 AM · Difficulty 10.6136 · 6,341,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d98bfd09f58649b4443f433788e59a368f18636baed3341ab7dcedade933298b

View on Chainz ↗

Height

#485,827

Difficulty

10.613550

Transactions

Size

429 B

Version

Bits

0a9d11a0

Nonce

656,209,074

Timestamp

4/11/2014, 7:01:22 AM

Confirmations

6,341,167

Mined by

⛏️ P2SHAHs5qUDbUEXDkb7rbuRKBk58iuJGfMmGNo

Merkle Root

f11fb1d7b99d5f7cbc0791fd1196c273bd1aab4ed7b5dfc607562412f5ea6dc2

Transactions (2)

Coinbase5c6738872dbe18…3a6ad90d04772b

1 in → 1 out8.8700 XPM111 B

AHs5qUDb…JGfMmGNo

40b164b36a88cf…0b9c9fcccbcc81

1 in → 2 out1800.0601 XPM226 B

ATgzG9Ep…FZz1rYRV AKSxfKfu…PrY2y58U

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.

2.520 × 10⁹⁸(99-digit number)

25209410971904157856…21353035816359839199

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

2.520 × 10⁹⁸(99-digit number)

25209410971904157856…21353035816359839199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.520 × 10⁹⁸(99-digit number)

25209410971904157856…21353035816359839201

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

5.041 × 10⁹⁸(99-digit number)

50418821943808315712…42706071632719678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.041 × 10⁹⁸(99-digit number)

50418821943808315712…42706071632719678401

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

1.008 × 10⁹⁹(100-digit number)

10083764388761663142…85412143265439356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.008 × 10⁹⁹(100-digit number)

10083764388761663142…85412143265439356801

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

2.016 × 10⁹⁹(100-digit number)

20167528777523326285…70824286530878713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.016 × 10⁹⁹(100-digit number)

20167528777523326285…70824286530878713601

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

4.033 × 10⁹⁹(100-digit number)

40335057555046652570…41648573061757427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.033 × 10⁹⁹(100-digit number)

40335057555046652570…41648573061757427201

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 #485,827

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