Block #602,556

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/26/2014, 9:15:52 AM · Difficulty 10.9132 · 6,199,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b368abcaf4dfb6e03fb949f0721bfca1c5386df3110695e6a65b39c5ae6eff54

Height

#602,556

Difficulty

10.913226

Transactions

3

Size

809 B

Version

2

Bits

0ae9c931

Nonce

137,933,045

Timestamp

6/26/2014, 9:15:52 AM

Confirmations

6,199,245

Merkle Root

425b181533a686c3d14b2dd5a6b1d6aee96e8b1c43e971ab54fa16aaab5b29b7
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.

7.127 × 10⁹⁸(99-digit number)
71278442755822824934…64671673235600002559
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
7.127 × 10⁹⁸(99-digit number)
71278442755822824934…64671673235600002559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.425 × 10⁹⁹(100-digit number)
14255688551164564986…29343346471200005119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.851 × 10⁹⁹(100-digit number)
28511377102329129973…58686692942400010239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.702 × 10⁹⁹(100-digit number)
57022754204658259947…17373385884800020479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.140 × 10¹⁰⁰(101-digit number)
11404550840931651989…34746771769600040959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.280 × 10¹⁰⁰(101-digit number)
22809101681863303978…69493543539200081919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.561 × 10¹⁰⁰(101-digit number)
45618203363726607957…38987087078400163839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.123 × 10¹⁰⁰(101-digit number)
91236406727453215915…77974174156800327679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.824 × 10¹⁰¹(102-digit number)
18247281345490643183…55948348313600655359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.649 × 10¹⁰¹(102-digit number)
36494562690981286366…11896696627201310719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.298 × 10¹⁰¹(102-digit number)
72989125381962572732…23793393254402621439
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:57,658,498 XPM·at block #6,801,800 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.