Block #603,494

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/27/2014, 2:41:31 AM · Difficulty 10.9114 · 6,192,130 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d15f5384792abcbb791f0aff766798c48910abb23c4f261c95cc5d7a13cb651

Height

#603,494

Difficulty

10.911442

Transactions

4

Size

1.15 KB

Version

2

Bits

0ae9544b

Nonce

418,142,680

Timestamp

6/27/2014, 2:41:31 AM

Confirmations

6,192,130

Merkle Root

bbc5f8b53d1621bfa5dc89da4d3975bff589bd2db9ce310c045e0153adc62cf1
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.

1.857 × 10⁹⁸(99-digit number)
18571908851400783138…34256702977264975359
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
1.857 × 10⁹⁸(99-digit number)
18571908851400783138…34256702977264975359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.714 × 10⁹⁸(99-digit number)
37143817702801566276…68513405954529950719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.428 × 10⁹⁸(99-digit number)
74287635405603132552…37026811909059901439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.485 × 10⁹⁹(100-digit number)
14857527081120626510…74053623818119802879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.971 × 10⁹⁹(100-digit number)
29715054162241253020…48107247636239605759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.943 × 10⁹⁹(100-digit number)
59430108324482506041…96214495272479211519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.188 × 10¹⁰⁰(101-digit number)
11886021664896501208…92428990544958423039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.377 × 10¹⁰⁰(101-digit number)
23772043329793002416…84857981089916846079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.754 × 10¹⁰⁰(101-digit number)
47544086659586004833…69715962179833692159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.508 × 10¹⁰⁰(101-digit number)
95088173319172009667…39431924359667384319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.901 × 10¹⁰¹(102-digit number)
19017634663834401933…78863848719334768639
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:57,609,059 XPM·at block #6,795,623 · updates every 60s
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