Block #423,686

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 2:29:13 PM · Difficulty 10.3788 · 6,381,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d78f72fec00520abe6207096173077935afbbe39d48bab70240c0720e9f07cb2

View on Chainz ↗

Height

#423,686

Difficulty

10.378835

Transactions

Size

1.10 KB

Version

Bits

0a60fb54

Nonce

168,512

Timestamp

2/28/2014, 2:29:13 PM

Confirmations

6,381,507

Mined by

⛏️ wsAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

db2aa8958c5816c067f718d75192d307da44521df8b1102344cc946a56340270

Transactions (5)

Coinbasecfff7d01ded339…1f7f6285cae728

1 in → 2 out9.3100 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

f0e8ce6d7cd86e…4766469f868bdf

1 in → 2 out7.1500 XPM227 B

AMWhfZow…EH5vsb34 ATBJHs8x…QQwBzmbj

93395e60c4682c…d9486c392d8b67

1 in → 2 out6.1627 XPM226 B

AXNVLKpH…GHdwoAxs AWoa918z…SSE4y7Hf

f94305785fce94…e17b601e804651

1 in → 2 out4.9862 XPM226 B

AZ8ovUF9…6ugkpVtm ALRq9aLC…s1nj8Vhi

5b5d320057f8bc…8e5a9195d83833

1 in → 2 out3.1624 XPM227 B

ASHt9j3u…GCWuP8QX AKvWCBdS…KRcoBvYr

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.

1.096 × 10⁹⁵(96-digit number)

10968330528305733261…79159411835546446999

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

1.096 × 10⁹⁵(96-digit number)

10968330528305733261…79159411835546446999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.096 × 10⁹⁵(96-digit number)

10968330528305733261…79159411835546447001

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

2.193 × 10⁹⁵(96-digit number)

21936661056611466523…58318823671092893999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.193 × 10⁹⁵(96-digit number)

21936661056611466523…58318823671092894001

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

4.387 × 10⁹⁵(96-digit number)

43873322113222933046…16637647342185787999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.387 × 10⁹⁵(96-digit number)

43873322113222933046…16637647342185788001

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

8.774 × 10⁹⁵(96-digit number)

87746644226445866092…33275294684371575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.774 × 10⁹⁵(96-digit number)

87746644226445866092…33275294684371576001

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

1.754 × 10⁹⁶(97-digit number)

17549328845289173218…66550589368743151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.754 × 10⁹⁶(97-digit number)

17549328845289173218…66550589368743152001

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