Block #470,896

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 5:55:21 AM · Difficulty 10.4295 · 6,323,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e5da664f58df8910c5c92b850d2759f05a1efb1ce0554af6f864bff9567e65b

View on Chainz ↗

Height

#470,896

Difficulty

10.429456

Transactions

Size

1.26 KB

Version

Bits

0a6df0d0

Nonce

5,868,152

Timestamp

4/2/2014, 5:55:21 AM

Confirmations

6,323,390

Merkle Root

34c5592c72574bcab95d406182771c437f4ba2576fa2e618962a7da5278001e4

Transactions (2)

Coinbased659db5137218b…ba438f4b26a976

1 in → 1 out9.2000 XPM109 B

AYLHuvcC…6agw2eUa

7d32fd03372100…89d18bb0782982

5 in → 15 out46.0800 XPM1.07 KB

AZRneJSc…cLnNgWaU AHbqA1Lc…6FYig9qr AYpANtX5…cpBRh2BL AeKNrjNj…1NEq95Ta AUthT9vU…E6Y5Rzws

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.

1.025 × 10⁹⁷(98-digit number)

10255213520631766942…70241249985530040319

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

1.025 × 10⁹⁷(98-digit number)

10255213520631766942…70241249985530040319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.025 × 10⁹⁷(98-digit number)

10255213520631766942…70241249985530040321

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

2.051 × 10⁹⁷(98-digit number)

20510427041263533885…40482499971060080639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.051 × 10⁹⁷(98-digit number)

20510427041263533885…40482499971060080641

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

4.102 × 10⁹⁷(98-digit number)

41020854082527067770…80964999942120161279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.102 × 10⁹⁷(98-digit number)

41020854082527067770…80964999942120161281

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

8.204 × 10⁹⁷(98-digit number)

82041708165054135540…61929999884240322559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.204 × 10⁹⁷(98-digit number)

82041708165054135540…61929999884240322561

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

1.640 × 10⁹⁸(99-digit number)

16408341633010827108…23859999768480645119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.640 × 10⁹⁸(99-digit number)

16408341633010827108…23859999768480645121

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