Block #2,960,629

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2018, 1:03:21 AM · Difficulty 11.3443 · 3,880,398 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cd61256e3455cfa73e73c02d2e032f4fecec5b1c3da320da59f1de23dd78fccd

Height

#2,960,629

Difficulty

11.344287

Transactions

2

Size

575 B

Version

2

Bits

0b58232a

Nonce

230,742,257

Timestamp

12/11/2018, 1:03:21 AM

Confirmations

3,880,398

Merkle Root

3ebcbe3b32924ff186f2a8b1c83742179a0a37f68f9014adecbc2d9247f5305b
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.

4.527 × 10⁹⁵(96-digit number)
45270836417085874282…76040662371616567201
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
4.527 × 10⁹⁵(96-digit number)
45270836417085874282…76040662371616567201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.054 × 10⁹⁵(96-digit number)
90541672834171748565…52081324743233134401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.810 × 10⁹⁶(97-digit number)
18108334566834349713…04162649486466268801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.621 × 10⁹⁶(97-digit number)
36216669133668699426…08325298972932537601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.243 × 10⁹⁶(97-digit number)
72433338267337398852…16650597945865075201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.448 × 10⁹⁷(98-digit number)
14486667653467479770…33301195891730150401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.897 × 10⁹⁷(98-digit number)
28973335306934959540…66602391783460300801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.794 × 10⁹⁷(98-digit number)
57946670613869919081…33204783566920601601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.158 × 10⁹⁸(99-digit number)
11589334122773983816…66409567133841203201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.317 × 10⁹⁸(99-digit number)
23178668245547967632…32819134267682406401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.635 × 10⁹⁸(99-digit number)
46357336491095935265…65638268535364812801
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:57,972,574 XPM·at block #6,841,026 · updates every 60s
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