Block #2,165,371

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2017, 3:26:43 AM · Difficulty 10.8984 · 4,650,837 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6550b703fb27ff3df64cff5040da93886e8bc8b8fd9837a4ddab72a829ed13b1

View on Chainz ↗

Height

#2,165,371

Difficulty

10.898408

Transactions

Size

6.96 KB

Version

Bits

0ae5fe0d

Nonce

275,237,669

Timestamp

6/18/2017, 3:26:43 AM

Confirmations

4,650,837

Mined by

⛏️ P2SHAPJjb1ATKuLp1jqkagZCFcMbXPtot8BUAT

Merkle Root

de37a48d57deb4ec55eb6ae382c8d5c6c338e9d9e692f4e9b793218fcf3a736b

Transactions (3)

Coinbasec20208f2377afd…ebf0501a51e322

1 in → 1 out8.4900 XPM109 B

APJjb1AT…tot8BUAT

54eb4777649957…34e8bf0cfd2ef6

45 in → 2 out518.1079 XPM6.58 KB

AWQnFkun…W2vjKb5L AdXSigFn…Xt9FMnbf

08c755d58fdd9c…c3624d5212b7c2

1 in → 2 out8.3900 XPM192 B

ASUN9jpU…fHk9MXzk ASdXKexa…kch59HW5

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.

6.970 × 10⁹⁵(96-digit number)

69707672615981604709…45790396211858935679

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

6.970 × 10⁹⁵(96-digit number)

69707672615981604709…45790396211858935679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.970 × 10⁹⁵(96-digit number)

69707672615981604709…45790396211858935681

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

1.394 × 10⁹⁶(97-digit number)

13941534523196320941…91580792423717871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.394 × 10⁹⁶(97-digit number)

13941534523196320941…91580792423717871361

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

2.788 × 10⁹⁶(97-digit number)

27883069046392641883…83161584847435742719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.788 × 10⁹⁶(97-digit number)

27883069046392641883…83161584847435742721

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

5.576 × 10⁹⁶(97-digit number)

55766138092785283767…66323169694871485439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.576 × 10⁹⁶(97-digit number)

55766138092785283767…66323169694871485441

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

1.115 × 10⁹⁷(98-digit number)

11153227618557056753…32646339389742970879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.115 × 10⁹⁷(98-digit number)

11153227618557056753…32646339389742970881

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 #2,165,371

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