Block #2,178,469

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2017, 3:10:37 AM · Difficulty 10.9263 · 4,662,050 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01b247a337be97d68468a0977d4a794dc3fd09380d86a883c04fb405285011ac

View on Chainz ↗

Height

#2,178,469

Difficulty

10.926259

Transactions

Size

426 B

Version

Bits

0aed1f4c

Nonce

418,035,774

Timestamp

6/26/2017, 3:10:37 AM

Confirmations

4,662,050

Mined by

⛏️ P2SHAUdscQjoEvZG9LCpr6r6QzxnkA8mvbpLMG

Merkle Root

e92fd269f9d7719f3a5566a462431f7fac9fbd6cca00ff8a0033bb7ef7536b31

Transactions (2)

Coinbase6b5fc493ccf055…975b384f28af70

1 in → 1 out8.3700 XPM110 B

AUdscQjo…8mvbpLMG

bacef591d640e9…58714c7e95d797

1 in → 2 out0.9800 XPM225 B

Ab9Jo4Ae…FQqsC7tm AXyMjoNd…Lapqjyzy

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.

2.239 × 10⁹⁶(97-digit number)

22396781406529531177…28365734835601269759

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

2.239 × 10⁹⁶(97-digit number)

22396781406529531177…28365734835601269759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.239 × 10⁹⁶(97-digit number)

22396781406529531177…28365734835601269761

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

4.479 × 10⁹⁶(97-digit number)

44793562813059062355…56731469671202539519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.479 × 10⁹⁶(97-digit number)

44793562813059062355…56731469671202539521

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

8.958 × 10⁹⁶(97-digit number)

89587125626118124710…13462939342405079039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.958 × 10⁹⁶(97-digit number)

89587125626118124710…13462939342405079041

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

1.791 × 10⁹⁷(98-digit number)

17917425125223624942…26925878684810158079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.791 × 10⁹⁷(98-digit number)

17917425125223624942…26925878684810158081

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

3.583 × 10⁹⁷(98-digit number)

35834850250447249884…53851757369620316159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.583 × 10⁹⁷(98-digit number)

35834850250447249884…53851757369620316161

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 #2,178,469

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