Block #469,895

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 1:30:28 PM · Difficulty 10.4280 · 6,322,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6183766e67f566a96ac7d8f8ddd55e042cb2c3df2b48cac4eea901b5b46a57e

View on Chainz ↗

Height

#469,895

Difficulty

10.427958

Transactions

Size

1.87 KB

Version

Bits

0a6d8eaa

Nonce

206,554

Timestamp

4/1/2014, 1:30:28 PM

Confirmations

6,322,068

Merkle Root

854d9f456db7e7ecb473e8c3bf5d363d805ee825ca1b8f8efe7b31e6b3204806

Transactions (4)

Coinbase248ce856fb69ae…6b4dd207539dfa

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

f79ef832b34f39…c58e7c2434a140

3 in → 2 out26.0062 XPM523 B

AbiDGesC…591TkzG8 ANQcyHXp…fYDKzWxK

a9a9efc2fc16b3…95993d9a6c29bd

6 in → 2 out0.9145 XPM968 B

AMuzaWBv…hZ6HZ3WJ AP1d1vcg…hPUk2Uru

49b6024e61d88b…138277d9ebab5b

1 in → 2 out4.6749 XPM226 B

AK4iFxWW…MWayPjXe AeKNrjNj…1NEq95Ta

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.

2.694 × 10⁹⁵(96-digit number)

26943383315429442443…50996670473465747999

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

2.694 × 10⁹⁵(96-digit number)

26943383315429442443…50996670473465747999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.694 × 10⁹⁵(96-digit number)

26943383315429442443…50996670473465748001

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

5.388 × 10⁹⁵(96-digit number)

53886766630858884886…01993340946931495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.388 × 10⁹⁵(96-digit number)

53886766630858884886…01993340946931496001

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

1.077 × 10⁹⁶(97-digit number)

10777353326171776977…03986681893862991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.077 × 10⁹⁶(97-digit number)

10777353326171776977…03986681893862992001

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

2.155 × 10⁹⁶(97-digit number)

21554706652343553954…07973363787725983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.155 × 10⁹⁶(97-digit number)

21554706652343553954…07973363787725984001

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

4.310 × 10⁹⁶(97-digit number)

43109413304687107909…15946727575451967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.310 × 10⁹⁶(97-digit number)

43109413304687107909…15946727575451968001

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