Block #468,847

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 7:08:35 PM · Difficulty 10.4323 · 6,327,102 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d981d5c83fb47c6cc5ef53dbd48bf2d847990b7826a1f4373c6ebf40115fc4da

View on Chainz ↗

Height

#468,847

Difficulty

10.432276

Transactions

Size

706 B

Version

Bits

0a6ea9aa

Nonce

52,724

Timestamp

3/31/2014, 7:08:35 PM

Confirmations

6,327,102

Mined by

⛏️ o'0AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

0d1327b0e61693e72fbe3c19aa0b56a78950e3e87767b84c5a21771c87a926de

Transactions (3)

Coinbase5f24695f4e0c79…68a1bfbe5af2a2

1 in → 3 out9.1900 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

33cbaedbee399d…4ef21af1b77dae

1 in → 2 out4.0785 XPM225 B

AX3tapEA…6hjxyaxk AMAn2RqT…WgyLvxav

fec624bc67742b…c587040dcec3ac

1 in → 2 out1.3296 XPM227 B

AWaxTsag…PL1cyPDP AcDkv4Nh…3YeXgBvi

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.

2.080 × 10⁹²(93-digit number)

20809119360045111899…16844702575329745919

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

2.080 × 10⁹²(93-digit number)

20809119360045111899…16844702575329745919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.080 × 10⁹²(93-digit number)

20809119360045111899…16844702575329745921

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

4.161 × 10⁹²(93-digit number)

41618238720090223798…33689405150659491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.161 × 10⁹²(93-digit number)

41618238720090223798…33689405150659491841

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

8.323 × 10⁹²(93-digit number)

83236477440180447596…67378810301318983679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.323 × 10⁹²(93-digit number)

83236477440180447596…67378810301318983681

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

1.664 × 10⁹³(94-digit number)

16647295488036089519…34757620602637967359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.664 × 10⁹³(94-digit number)

16647295488036089519…34757620602637967361

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

3.329 × 10⁹³(94-digit number)

33294590976072179038…69515241205275934719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.329 × 10⁹³(94-digit number)

33294590976072179038…69515241205275934721

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