Block #2,369,847

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2017, 3:57:39 PM · Difficulty 10.8934 · 4,469,401 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8cd170e150d0dc0c2589d3e131f09dd1914b0386de19336ca709a051028c48f9

View on Chainz ↗

Height

#2,369,847

Difficulty

10.893416

Transactions

Size

2.08 KB

Version

Bits

0ae4b6ec

Nonce

833,394,067

Timestamp

11/7/2017, 3:57:39 PM

Confirmations

4,469,401

Mined by

⛏️ P2SHASB2FXwrN7YV6DQwovo2qL35zpcVkAhFkU

Merkle Root

00db17af15e9b6b29362131c3257d8fe7673e62e75af29c32055137c1c219994

Transactions (3)

Coinbase67a4b091f614a3…e070f392e3c519

1 in → 1 out8.4300 XPM109 B

ASB2FXwr…cVkAhFkU

500c9a32044eb1…66ecf2435d8283

6 in → 2 out737.3777 XPM965 B

AXE9b92F…RkxofpC1 AMYPZmyt…hb7ZPY5w

d6b6a0fc8379b2…c9f33e26f5cbe2

6 in → 2 out14.8999 XPM967 B

AJJdT41K…H1216oD8 AGEqGmTi…Ff83XFFE

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.

4.113 × 10⁹⁵(96-digit number)

41135371279152797303…24739426994534805759

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

4.113 × 10⁹⁵(96-digit number)

41135371279152797303…24739426994534805759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.113 × 10⁹⁵(96-digit number)

41135371279152797303…24739426994534805761

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

8.227 × 10⁹⁵(96-digit number)

82270742558305594606…49478853989069611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.227 × 10⁹⁵(96-digit number)

82270742558305594606…49478853989069611521

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

1.645 × 10⁹⁶(97-digit number)

16454148511661118921…98957707978139223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.645 × 10⁹⁶(97-digit number)

16454148511661118921…98957707978139223041

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

3.290 × 10⁹⁶(97-digit number)

32908297023322237842…97915415956278446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.290 × 10⁹⁶(97-digit number)

32908297023322237842…97915415956278446081

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

6.581 × 10⁹⁶(97-digit number)

65816594046644475684…95830831912556892159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.581 × 10⁹⁶(97-digit number)

65816594046644475684…95830831912556892161

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 #2,369,847

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