Block #379,414

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2014, 12:49:35 PM · Difficulty 10.4167 · 6,416,748 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
282201cd8e1ea87472d7d7661ba1ecb4ef48521c639a7ed7e4f7d36f4a59b4d6

Height

#379,414

Difficulty

10.416736

Transactions

3

Size

660 B

Version

2

Bits

0a6aaf39

Nonce

72,424

Timestamp

1/28/2014, 12:49:35 PM

Confirmations

6,416,748

Merkle Root

bf4f1c53e8bc4ec4665096f3077a578287335e1c99b0d6963ab3c808cfae9cb8
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.

2.071 × 10⁹⁸(99-digit number)
20712231103204861797…25428673716801368801
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
2.071 × 10⁹⁸(99-digit number)
20712231103204861797…25428673716801368801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.142 × 10⁹⁸(99-digit number)
41424462206409723594…50857347433602737601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.284 × 10⁹⁸(99-digit number)
82848924412819447188…01714694867205475201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.656 × 10⁹⁹(100-digit number)
16569784882563889437…03429389734410950401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.313 × 10⁹⁹(100-digit number)
33139569765127778875…06858779468821900801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.627 × 10⁹⁹(100-digit number)
66279139530255557750…13717558937643801601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.325 × 10¹⁰⁰(101-digit number)
13255827906051111550…27435117875287603201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.651 × 10¹⁰⁰(101-digit number)
26511655812102223100…54870235750575206401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.302 × 10¹⁰⁰(101-digit number)
53023311624204446200…09740471501150412801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.060 × 10¹⁰¹(102-digit number)
10604662324840889240…19480943002300825601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.120 × 10¹⁰¹(102-digit number)
21209324649681778480…38961886004601651201
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:57,613,293 XPM·at block #6,796,161 · updates every 60s
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