Block #1,091,578

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/6/2015, 1:16:26 AM · Difficulty 10.7366 · 5,722,716 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3e7c4812334afc30323293abcd2d4045eada8726b421edf1808703d8baf4d7ff

Height

#1,091,578

Difficulty

10.736565

Transactions

6

Size

1.37 KB

Version

2

Bits

0abc8f8c

Nonce

85,568

Timestamp

6/6/2015, 1:16:26 AM

Confirmations

5,722,716

Merkle Root

d2ab2d5bdce83d3ffa743ef3982792b4980bde5d06a23498b937cfc83e68020f
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.

8.084 × 10⁹⁶(97-digit number)
80849989555075690024…26100303001349300479
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
8.084 × 10⁹⁶(97-digit number)
80849989555075690024…26100303001349300479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.616 × 10⁹⁷(98-digit number)
16169997911015138004…52200606002698600959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.233 × 10⁹⁷(98-digit number)
32339995822030276009…04401212005397201919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.467 × 10⁹⁷(98-digit number)
64679991644060552019…08802424010794403839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.293 × 10⁹⁸(99-digit number)
12935998328812110403…17604848021588807679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.587 × 10⁹⁸(99-digit number)
25871996657624220807…35209696043177615359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.174 × 10⁹⁸(99-digit number)
51743993315248441615…70419392086355230719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.034 × 10⁹⁹(100-digit number)
10348798663049688323…40838784172710461439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.069 × 10⁹⁹(100-digit number)
20697597326099376646…81677568345420922879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.139 × 10⁹⁹(100-digit number)
41395194652198753292…63355136690841845759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
8.279 × 10⁹⁹(100-digit number)
82790389304397506585…26710273381683691519
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,758,415 XPM·at block #6,814,293 · updates every 60s
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