Block #469,598

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 8:31:17 AM · Difficulty 10.4273 · 6,355,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8485b744a19743f9f6d92dab5e1c8c61c53cca6fcdcb886869bf5de46a4ef60f

View on Chainz ↗

Height

#469,598

Difficulty

10.427291

Transactions

Size

1.08 KB

Version

Bits

0a6d62f6

Nonce

22,057,183

Timestamp

4/1/2014, 8:31:17 AM

Confirmations

6,355,224

Mined by

⛏️ P2SHAPDBYGA529oHfBsJuXTkaMM6BPkFaThEzy

Merkle Root

699dfdc0c17e031f7b946bed0bfb40d4d45535c3e060031620191f6afa3c2c43

Transactions (5)

Coinbase0274054fa0d646…a83047eb69d9bb

1 in → 1 out9.2200 XPM109 B

APDBYGA5…kFaThEzy

69d563ac5581bb…245b8537bbb414

1 in → 2 out8.1680 XPM226 B

AHcJb2mR…d1XLR6RJ AYFxzicp…jeAdgy2P

5a8b02e3202529…b974e77d300a6a

1 in → 2 out8.1656 XPM226 B

Abz9iBqs…EC85r3Lj AT6Euv26…ZvkiTxo7

f31ad4ce389058…88b33318ae5b4a

1 in → 2 out3.1069 XPM226 B

AGoNi5MG…ZDc5F7vQ AQr4g22L…cCYdhBvN

f73a3be8ad7f09…01689519c6d353

1 in → 2 out1.5162 XPM226 B

ATdtomYD…mXhzxvF9 Ac942eYg…WZFJgxRz

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.

4.425 × 10⁹⁷(98-digit number)

44252474271054011824…07699100668284538879

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

4.425 × 10⁹⁷(98-digit number)

44252474271054011824…07699100668284538879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.425 × 10⁹⁷(98-digit number)

44252474271054011824…07699100668284538881

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

8.850 × 10⁹⁷(98-digit number)

88504948542108023649…15398201336569077759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.850 × 10⁹⁷(98-digit number)

88504948542108023649…15398201336569077761

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

1.770 × 10⁹⁸(99-digit number)

17700989708421604729…30796402673138155519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.770 × 10⁹⁸(99-digit number)

17700989708421604729…30796402673138155521

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

3.540 × 10⁹⁸(99-digit number)

35401979416843209459…61592805346276311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.540 × 10⁹⁸(99-digit number)

35401979416843209459…61592805346276311041

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

7.080 × 10⁹⁸(99-digit number)

70803958833686418919…23185610692552622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.080 × 10⁹⁸(99-digit number)

70803958833686418919…23185610692552622081

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 #469,598

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