Block #327,095

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 7:29:40 AM · Difficulty 10.1784 · 6,466,979 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d0ee1164d9bc2bf0869b49392dcc6a170f14ef2c9e051c50dee8ba04ccf2f92

View on Chainz ↗

Height

#327,095

Difficulty

10.178403

Transactions

Size

1.01 KB

Version

Bits

0a2dabd7

Nonce

261,836

Timestamp

12/24/2013, 7:29:40 AM

Confirmations

6,466,979

Merkle Root

cb71588fceb246dbcade5339809d690bae65933de94e279e62d9664c350a941c

Transactions (1)

Coinbasecb71588fceb246…d9664c350a941c

1 in → 26 out9.6400 XPM947 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR ARy21REr…6pBWtQJ2 AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz

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.

1.222 × 10⁹⁶(97-digit number)

12222201810717169571…89525895092605647709

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

1.222 × 10⁹⁶(97-digit number)

12222201810717169571…89525895092605647709

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.222 × 10⁹⁶(97-digit number)

12222201810717169571…89525895092605647711

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

2.444 × 10⁹⁶(97-digit number)

24444403621434339143…79051790185211295419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.444 × 10⁹⁶(97-digit number)

24444403621434339143…79051790185211295421

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

4.888 × 10⁹⁶(97-digit number)

48888807242868678286…58103580370422590839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.888 × 10⁹⁶(97-digit number)

48888807242868678286…58103580370422590841

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

9.777 × 10⁹⁶(97-digit number)

97777614485737356572…16207160740845181679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.777 × 10⁹⁶(97-digit number)

97777614485737356572…16207160740845181681

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

1.955 × 10⁹⁷(98-digit number)

19555522897147471314…32414321481690363359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.955 × 10⁹⁷(98-digit number)

19555522897147471314…32414321481690363361

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