Block #1,365,263

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2015, 11:52:13 AM · Difficulty 10.8457 · 5,448,777 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b55e799fa255e9b9d43de486245f640d361ca3dc0c694a8c930f9742d52386fc

Height

#1,365,263

Difficulty

10.845693

Transactions

2

Size

872 B

Version

2

Bits

0ad87f4f

Nonce

118,213,669

Timestamp

12/11/2015, 11:52:13 AM

Confirmations

5,448,777

Merkle Root

be3c223525c30ba3a6f2a30b0e63910b844ba9eaa92c3a593a14a20ca729520c
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.

6.063 × 10⁹⁶(97-digit number)
60639957513479202148…49615399369333678081
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
6.063 × 10⁹⁶(97-digit number)
60639957513479202148…49615399369333678081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.212 × 10⁹⁷(98-digit number)
12127991502695840429…99230798738667356161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.425 × 10⁹⁷(98-digit number)
24255983005391680859…98461597477334712321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.851 × 10⁹⁷(98-digit number)
48511966010783361718…96923194954669424641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.702 × 10⁹⁷(98-digit number)
97023932021566723437…93846389909338849281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.940 × 10⁹⁸(99-digit number)
19404786404313344687…87692779818677698561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.880 × 10⁹⁸(99-digit number)
38809572808626689374…75385559637355397121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.761 × 10⁹⁸(99-digit number)
77619145617253378749…50771119274710794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.552 × 10⁹⁹(100-digit number)
15523829123450675749…01542238549421588481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.104 × 10⁹⁹(100-digit number)
31047658246901351499…03084477098843176961
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:57,756,395 XPM·at block #6,814,039 · updates every 60s
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