Block #2,169,060

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/20/2017, 4:44:37 PM · Difficulty 10.8987 · 4,662,568 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67afdd0af4bcd6bf8c9211bca43bb9a6beba67837a8f163498bb97f7e4f1f4de

View on Chainz ↗

Height

#2,169,060

Difficulty

10.898735

Transactions

Size

11.30 KB

Version

Bits

0ae61380

Nonce

1,222,542,479

Timestamp

6/20/2017, 4:44:37 PM

Confirmations

4,662,568

Mined by

⛏️ P2SHAZEBfJf2mG45ELfSt9Tp62pVfukA5vi9Bi

Merkle Root

a8faadbfd8b2404d4e4f435b9e555880cdb6493b5ed530bfe958948fd317f24e

Transactions (2)

Coinbasec6754012d53404…ff498deced01f4

1 in → 1 out8.5300 XPM110 B

AZEBfJf2…kA5vi9Bi

2af6d97084bbfc…1572f927bebe16

76 in → 3 out11977.4001 XPM11.10 KB

AcxhUhX6…N8N8w2tm AJ8nMmse…xNBF2kBg APwqQBGJ…gCNBgvF2

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.

3.078 × 10⁹⁴(95-digit number)

30780455321870944669…00824933237262572839

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

3.078 × 10⁹⁴(95-digit number)

30780455321870944669…00824933237262572839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.078 × 10⁹⁴(95-digit number)

30780455321870944669…00824933237262572841

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

6.156 × 10⁹⁴(95-digit number)

61560910643741889339…01649866474525145679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.156 × 10⁹⁴(95-digit number)

61560910643741889339…01649866474525145681

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

1.231 × 10⁹⁵(96-digit number)

12312182128748377867…03299732949050291359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.231 × 10⁹⁵(96-digit number)

12312182128748377867…03299732949050291361

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

2.462 × 10⁹⁵(96-digit number)

24624364257496755735…06599465898100582719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.462 × 10⁹⁵(96-digit number)

24624364257496755735…06599465898100582721

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

4.924 × 10⁹⁵(96-digit number)

49248728514993511471…13198931796201165439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.924 × 10⁹⁵(96-digit number)

49248728514993511471…13198931796201165441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.849 × 10⁹⁵(96-digit number)

98497457029987022942…26397863592402330879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,169,060

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