Block #318,217

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 5:18:08 AM · Difficulty 10.1588 · 6,472,724 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3da39b4e82d2317bb743510caaf3711f066ae3ccfbf177f6940027eabcb3f652

View on Chainz ↗

Height

#318,217

Difficulty

10.158764

Transactions

Size

766 B

Version

Bits

0a28a4ba

Nonce

676

Timestamp

12/18/2013, 5:18:08 AM

Confirmations

6,472,724

Merkle Root

ebf65b34380c2fb1bea49893883f08d544a6be5c605fc75d447883ce8d43c2fa

Transactions (3)

Coinbaseb657afd714c7df…51da3104fc0443

1 in → 1 out9.7000 XPM109 B

AWT4FajA…7qUxCsaJ

b8968cfe276af0…e02c7cae225c25

1 in → 1 out3.0430 XPM191 B

AePUc49t…4zC5VvXd

7bfe91be950c2d…37f0e1d6d6588a

2 in → 2 out1.1271 XPM376 B

AHKRLU1g…gVTAoWox AGB3HZRH…7ZkMh8ic

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.

1.956 × 10⁹⁵(96-digit number)

19565077653701895485…85732727306956177299

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

1.956 × 10⁹⁵(96-digit number)

19565077653701895485…85732727306956177299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.956 × 10⁹⁵(96-digit number)

19565077653701895485…85732727306956177301

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

3.913 × 10⁹⁵(96-digit number)

39130155307403790970…71465454613912354599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.913 × 10⁹⁵(96-digit number)

39130155307403790970…71465454613912354601

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

7.826 × 10⁹⁵(96-digit number)

78260310614807581941…42930909227824709199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.826 × 10⁹⁵(96-digit number)

78260310614807581941…42930909227824709201

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

1.565 × 10⁹⁶(97-digit number)

15652062122961516388…85861818455649418399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.565 × 10⁹⁶(97-digit number)

15652062122961516388…85861818455649418401

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

3.130 × 10⁹⁶(97-digit number)

31304124245923032776…71723636911298836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.130 × 10⁹⁶(97-digit number)

31304124245923032776…71723636911298836801

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