Block #605,670

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/28/2014, 4:15:43 PM · Difficulty 10.9101 · 6,204,925 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
667f21ebe65e97c9cff2aeabc06875efabad305e618e7987c8da21c9a33b09ea

Height

#605,670

Difficulty

10.910100

Transactions

5

Size

10.71 KB

Version

2

Bits

0ae8fc50

Nonce

72,016,086

Timestamp

6/28/2014, 4:15:43 PM

Confirmations

6,204,925

Merkle Root

757f94ef63c4e49c1920426231bb77f074c51c02c7a3748d77917e5791a74b59
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.

5.529 × 10⁹⁹(100-digit number)
55299175702956701963…46883884136519813121
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
5.529 × 10⁹⁹(100-digit number)
55299175702956701963…46883884136519813121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.105 × 10¹⁰⁰(101-digit number)
11059835140591340392…93767768273039626241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.211 × 10¹⁰⁰(101-digit number)
22119670281182680785…87535536546079252481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.423 × 10¹⁰⁰(101-digit number)
44239340562365361570…75071073092158504961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.847 × 10¹⁰⁰(101-digit number)
88478681124730723141…50142146184317009921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.769 × 10¹⁰¹(102-digit number)
17695736224946144628…00284292368634019841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.539 × 10¹⁰¹(102-digit number)
35391472449892289256…00568584737268039681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.078 × 10¹⁰¹(102-digit number)
70782944899784578512…01137169474536079361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.415 × 10¹⁰²(103-digit number)
14156588979956915702…02274338949072158721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.831 × 10¹⁰²(103-digit number)
28313177959913831405…04548677898144317441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.662 × 10¹⁰²(103-digit number)
56626355919827662810…09097355796288634881
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:57,728,847 XPM·at block #6,810,594 · updates every 60s
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