Block #84,378

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 7:08:42 PM · Difficulty 9.2717 · 6,729,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9103f3b593af5444bc600ca644c65bdb6d06a3cece61eb29d7dc7bc59c93af31

View on Chainz ↗

Height

#84,378

Difficulty

9.271660

Transactions

Size

207 B

Version

Bits

09458b89

Nonce

76,691

Timestamp

7/26/2013, 7:08:42 PM

Confirmations

6,729,662

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

fe699a0e566321ab22c767040e060b77fb33bafeda3fe1f3f8cc988643fdb088

Transactions (1)

Coinbasefe699a0e566321…cc988643fdb088

1 in → 1 out11.6200 XPM109 B

AeEXQxqG…J2q5dxWc

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.

5.995 × 10¹¹⁴(115-digit number)

59950877953238657763…30001386752535916249

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

5.995 × 10¹¹⁴(115-digit number)

59950877953238657763…30001386752535916249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.995 × 10¹¹⁴(115-digit number)

59950877953238657763…30001386752535916251

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

1.199 × 10¹¹⁵(116-digit number)

11990175590647731552…60002773505071832499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.199 × 10¹¹⁵(116-digit number)

11990175590647731552…60002773505071832501

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

2.398 × 10¹¹⁵(116-digit number)

23980351181295463105…20005547010143664999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.398 × 10¹¹⁵(116-digit number)

23980351181295463105…20005547010143665001

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

4.796 × 10¹¹⁵(116-digit number)

47960702362590926210…40011094020287329999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.796 × 10¹¹⁵(116-digit number)

47960702362590926210…40011094020287330001

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

9.592 × 10¹¹⁵(116-digit number)

95921404725181852420…80022188040574659999

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

Block #84,378

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