Block #78,351

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 7:14:31 PM · Difficulty 9.2314 · 6,717,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f74c2079b558432d6d135d6432ddf7c2813c619ea5138e5a359a60f19a6860d0

View on Chainz ↗

Height

#78,351

Difficulty

9.231441

Transactions

Size

203 B

Version

Bits

093b3fbf

Nonce

196

Timestamp

7/22/2013, 7:14:31 PM

Confirmations

6,717,712

Mined by

⛏️ P2SHAK1JUKWLjkgQU8N3MsSKyKCPeAoPR4rN5o

Merkle Root

2f63aa14bd72624ab5cabff609a649e410867841841d661fe7b2d51876b4a506

Transactions (1)

Coinbase2f63aa14bd7262…b2d51876b4a506

1 in → 1 out11.7200 XPM110 B

AK1JUKWL…oPR4rN5o

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.

2.326 × 10¹⁰¹(102-digit number)

23268807247965117870…01241168087748535599

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

2.326 × 10¹⁰¹(102-digit number)

23268807247965117870…01241168087748535599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.326 × 10¹⁰¹(102-digit number)

23268807247965117870…01241168087748535601

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

4.653 × 10¹⁰¹(102-digit number)

46537614495930235741…02482336175497071199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.653 × 10¹⁰¹(102-digit number)

46537614495930235741…02482336175497071201

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

9.307 × 10¹⁰¹(102-digit number)

93075228991860471482…04964672350994142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.307 × 10¹⁰¹(102-digit number)

93075228991860471482…04964672350994142401

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

1.861 × 10¹⁰²(103-digit number)

18615045798372094296…09929344701988284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.861 × 10¹⁰²(103-digit number)

18615045798372094296…09929344701988284801

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

3.723 × 10¹⁰²(103-digit number)

37230091596744188592…19858689403976569599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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