Block #468,159

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 7:56:10 AM · Difficulty 10.4302 · 6,349,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

016597be3d40be8c3ac8ce24e20065ed7b35c835679b8c8c123a440b980638e0

View on Chainz ↗

Height

#468,159

Difficulty

10.430197

Transactions

Size

1.49 KB

Version

Bits

0a6e2167

Nonce

52,891

Timestamp

3/31/2014, 7:56:10 AM

Confirmations

6,349,660

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

97ee806c39d00284b44795bb080da9628bfe6c8670387f8a5e01d1b98e4edf80

Transactions (2)

Coinbase1a770221148877…42a22a5732ebd9

1 in → 22 out9.1900 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AUFKXvnz…342ApNcm AdoqUYAy…tJ482T9b

f8f81eb837f410…0f89cb4e7defb4

3 in → 7 out19.0448 XPM624 B

AUAeLXTf…CrTX8hGw AT17PSFn…faxELw2p AMLz4Dj6…KFvw5cVk AdjVuW2o…RiqZiW4R 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.

3.332 × 10⁹⁸(99-digit number)

33324284985630541706…42093003653114719999

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

3.332 × 10⁹⁸(99-digit number)

33324284985630541706…42093003653114719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.332 × 10⁹⁸(99-digit number)

33324284985630541706…42093003653114720001

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

6.664 × 10⁹⁸(99-digit number)

66648569971261083412…84186007306229439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.664 × 10⁹⁸(99-digit number)

66648569971261083412…84186007306229440001

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

1.332 × 10⁹⁹(100-digit number)

13329713994252216682…68372014612458879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.332 × 10⁹⁹(100-digit number)

13329713994252216682…68372014612458880001

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

2.665 × 10⁹⁹(100-digit number)

26659427988504433365…36744029224917759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.665 × 10⁹⁹(100-digit number)

26659427988504433365…36744029224917760001

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

5.331 × 10⁹⁹(100-digit number)

53318855977008866730…73488058449835519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.331 × 10⁹⁹(100-digit number)

53318855977008866730…73488058449835520001

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 #468,159

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