Block #2,177,159

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 10:10:29 AM · Difficulty 10.9219 · 4,637,141 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e5436fb959d4d62d794d9f5619e887c52ba7a325b92d90553c998297d577247

View on Chainz ↗

Height

#2,177,159

Difficulty

10.921862

Transactions

Size

574 B

Version

Bits

0aebff1e

Nonce

631,519,222

Timestamp

6/25/2017, 10:10:29 AM

Confirmations

4,637,141

Mined by

⛏️ P2SHAVjvVgcKJsGiG8pveYudB8isvUg7zcvDZL

Merkle Root

b7720e27a1c90c46fe5b550ac86340df9eee0395b4831fd0f088100b5ea83408

Transactions (2)

Coinbase4bd8b40f0da08f…88ea65e50fdebc

1 in → 1 out8.3800 XPM109 B

AVjvVgcK…g7zcvDZL

75bcccc1fa4b7f…25b7931f48a1b2

2 in → 2 out498.6105 XPM374 B

AdDMFSsZ…q9QGnJ7m AVB8Kqgj…zUanL8Tf

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.

1.919 × 10⁹⁷(98-digit number)

19195554876935627910…63636483739081277439

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

1.919 × 10⁹⁷(98-digit number)

19195554876935627910…63636483739081277439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.919 × 10⁹⁷(98-digit number)

19195554876935627910…63636483739081277441

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

3.839 × 10⁹⁷(98-digit number)

38391109753871255820…27272967478162554879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.839 × 10⁹⁷(98-digit number)

38391109753871255820…27272967478162554881

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

7.678 × 10⁹⁷(98-digit number)

76782219507742511640…54545934956325109759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.678 × 10⁹⁷(98-digit number)

76782219507742511640…54545934956325109761

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

1.535 × 10⁹⁸(99-digit number)

15356443901548502328…09091869912650219519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.535 × 10⁹⁸(99-digit number)

15356443901548502328…09091869912650219521

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

3.071 × 10⁹⁸(99-digit number)

30712887803097004656…18183739825300439039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.071 × 10⁹⁸(99-digit number)

30712887803097004656…18183739825300439041

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 #2,177,159

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