Block #492,052

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 9:10:40 PM · Difficulty 10.6876 · 6,314,696 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65f0d9fca53e25a6cf16100ee57de5fdcd8d5f6ca22bf999fd4a9330105185f5

View on Chainz ↗

Height

#492,052

Difficulty

10.687556

Transactions

Size

1.78 KB

Version

Bits

0ab003a8

Nonce

204,066,647

Timestamp

4/14/2014, 9:10:40 PM

Confirmations

6,314,696

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c1e55e278b586520de21384a80d9bf1c37a5909ccb8e33178a8923f45a317f23

Transactions (4)

Coinbase254fba530a5e28…bc7d7aa5b4c76d

1 in → 1 out8.7700 XPM116 B

AbwWkWZt…kawDhufa

c610b08e6b5d03…72906fbcee981d

2 in → 2 out17.5900 XPM305 B

AP1WbFPp…9YsXTY23 ATx8iQ8h…XbxyuQRB

5e2c22d4c5d8ae…73a8dc2dbdca49

2 in → 2 out17.5800 XPM306 B

ATmyPvbe…zEwtDuMa AWTXTqyv…wU6unC9A

ff618f59474176…ee362ea5bb2ec9

3 in → 16 out26.4400 XPM999 B

AGaJoZZM…uF5cjxJ1 AKzv8KjF…W6FeM9j1 AMz7QSWk…beNvX35p AZVposES…iGjyE5ZN AbNyp4U8…S5E4e4Ax

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.

3.902 × 10⁹⁸(99-digit number)

39029435859942558163…22976258255197499999

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

3.902 × 10⁹⁸(99-digit number)

39029435859942558163…22976258255197499999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.902 × 10⁹⁸(99-digit number)

39029435859942558163…22976258255197500001

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

7.805 × 10⁹⁸(99-digit number)

78058871719885116326…45952516510394999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.805 × 10⁹⁸(99-digit number)

78058871719885116326…45952516510395000001

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

1.561 × 10⁹⁹(100-digit number)

15611774343977023265…91905033020789999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.561 × 10⁹⁹(100-digit number)

15611774343977023265…91905033020790000001

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

3.122 × 10⁹⁹(100-digit number)

31223548687954046530…83810066041579999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.122 × 10⁹⁹(100-digit number)

31223548687954046530…83810066041580000001

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

6.244 × 10⁹⁹(100-digit number)

62447097375908093061…67620132083159999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.244 × 10⁹⁹(100-digit number)

62447097375908093061…67620132083160000001

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 #492,052

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