Block #1,442,577

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2016, 6:43:21 PM · Difficulty 10.7600 · 5,367,184 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
344ded5453304f3db0582da4b97cf2b4ea6e853c3586c381a6b9a3bfbd4cb179

Height

#1,442,577

Difficulty

10.760007

Transactions

3

Size

3.79 KB

Version

2

Bits

0ac28fd4

Nonce

255,505,650

Timestamp

2/4/2016, 6:43:21 PM

Confirmations

5,367,184

Merkle Root

da3478372afd2a0ecb4b57026f3df05d3b4f40b5c6fc03514e478395ced67a02
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.

3.833 × 10⁹⁴(95-digit number)
38338522395537478555…57007845424992439001
Discovered Prime Numbers
p_k = 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.

1
origin + 1
3.833 × 10⁹⁴(95-digit number)
38338522395537478555…57007845424992439001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.667 × 10⁹⁴(95-digit number)
76677044791074957111…14015690849984878001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.533 × 10⁹⁵(96-digit number)
15335408958214991422…28031381699969756001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.067 × 10⁹⁵(96-digit number)
30670817916429982844…56062763399939512001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.134 × 10⁹⁵(96-digit number)
61341635832859965689…12125526799879024001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.226 × 10⁹⁶(97-digit number)
12268327166571993137…24251053599758048001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.453 × 10⁹⁶(97-digit number)
24536654333143986275…48502107199516096001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.907 × 10⁹⁶(97-digit number)
49073308666287972551…97004214399032192001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.814 × 10⁹⁶(97-digit number)
98146617332575945103…94008428798064384001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.962 × 10⁹⁷(98-digit number)
19629323466515189020…88016857596128768001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.925 × 10⁹⁷(98-digit number)
39258646933030378041…76033715192257536001
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 Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,722,174 XPM·at block #6,809,760 · updates every 60s
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