Block #420,236

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 6:17:54 AM · Difficulty 10.3679 · 6,374,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a9cede827bbbeaecb9d80bd87e52001ac6930962e209601d5d2e1736a54f24b

View on Chainz ↗

Height

#420,236

Difficulty

10.367918

Transactions

Size

12.90 KB

Version

Bits

0a5e2fdd

Nonce

97,135

Timestamp

2/26/2014, 6:17:54 AM

Confirmations

6,374,366

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9b2b998834ab5f7a6bbe578ba5ad0fa965ecb17650fff4cc797875995a3ad12b

Transactions (4)

Coinbase98fad92b97f24d…0653b52b4f0202

1 in → 1 out9.4406 XPM110 B

AeKNrjNj…1NEq95Ta

f5f36da0ed0c72…7d973c9814f32a

1 in → 2 out9.1900 XPM226 B

AKdWt3ZZ…Lw3PdnZY AajzSvte…V7BMBiST

fbbb56b96b00f9…2ff3771244f721

8 in → 20 out66.2541 XPM1.60 KB

AdLr128r…uPvGsfSB AVETTRcK…AAGuMVQh AM7G6Uj2…1GLhCtA1 AZJ31Mao…gCve1AhC AXq1FUZY…39C33und

1642ef32b00b02…a37210b0ad2202

75 in → 1 out63.6200 XPM10.89 KB

AT6XraPv…6QRxJMf9

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.

7.110 × 10⁹⁸(99-digit number)

71101777399832209979…86649766173993983999

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

7.110 × 10⁹⁸(99-digit number)

71101777399832209979…86649766173993983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.110 × 10⁹⁸(99-digit number)

71101777399832209979…86649766173993984001

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

1.422 × 10⁹⁹(100-digit number)

14220355479966441995…73299532347987967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.422 × 10⁹⁹(100-digit number)

14220355479966441995…73299532347987968001

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

2.844 × 10⁹⁹(100-digit number)

28440710959932883991…46599064695975935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.844 × 10⁹⁹(100-digit number)

28440710959932883991…46599064695975936001

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

5.688 × 10⁹⁹(100-digit number)

56881421919865767983…93198129391951871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.688 × 10⁹⁹(100-digit number)

56881421919865767983…93198129391951872001

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

1.137 × 10¹⁰⁰(101-digit number)

11376284383973153596…86396258783903743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.137 × 10¹⁰⁰(101-digit number)

11376284383973153596…86396258783903744001

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