Block #1,379,064

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/21/2015, 7:36:39 PM · Difficulty 10.8100 · 5,437,564 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37442a9cca8aca3b86518ddd4a6f2a391236dfc267f7a2e4af823c7ac0971dcb

Height

#1,379,064

Difficulty

10.809997

Transactions

2

Size

1.57 KB

Version

2

Bits

0acf5bfa

Nonce

1,736,263,814

Timestamp

12/21/2015, 7:36:39 PM

Confirmations

5,437,564

Merkle Root

c3c421d200e29f7e4eaf992f8e8731f2bc0fadc31240d0ba588145e2a82707bf
Transactions (2)
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.

2.335 × 10⁹⁵(96-digit number)
23354649174767297164…29159001878289334401
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
2.335 × 10⁹⁵(96-digit number)
23354649174767297164…29159001878289334401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.670 × 10⁹⁵(96-digit number)
46709298349534594329…58318003756578668801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.341 × 10⁹⁵(96-digit number)
93418596699069188659…16636007513157337601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.868 × 10⁹⁶(97-digit number)
18683719339813837731…33272015026314675201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.736 × 10⁹⁶(97-digit number)
37367438679627675463…66544030052629350401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.473 × 10⁹⁶(97-digit number)
74734877359255350927…33088060105258700801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.494 × 10⁹⁷(98-digit number)
14946975471851070185…66176120210517401601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.989 × 10⁹⁷(98-digit number)
29893950943702140370…32352240421034803201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.978 × 10⁹⁷(98-digit number)
59787901887404280741…64704480842069606401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.195 × 10⁹⁸(99-digit number)
11957580377480856148…29408961684139212801
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,777,145 XPM·at block #6,816,627 · updates every 60s
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