Block #569,856

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/31/2014, 10:45:25 AM · Difficulty 10.9647 · 6,245,225 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be479cfb6a5fc54c275e34b35711aeaf1521038ac554142dd1292701274ae89d

Height

#569,856

Difficulty

10.964668

Transactions

3

Size

1.79 KB

Version

2

Bits

0af6f47b

Nonce

534,480,217

Timestamp

5/31/2014, 10:45:25 AM

Confirmations

6,245,225

Merkle Root

1c35dfbc2a22638bbb4022ae232a344b2a6a47873d72d898cd9e4ca6641a1f9a
Transactions (3)
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.

9.681 × 10⁹⁹(100-digit number)
96810851600975742451…70501557704884254721
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
9.681 × 10⁹⁹(100-digit number)
96810851600975742451…70501557704884254721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.936 × 10¹⁰⁰(101-digit number)
19362170320195148490…41003115409768509441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.872 × 10¹⁰⁰(101-digit number)
38724340640390296980…82006230819537018881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.744 × 10¹⁰⁰(101-digit number)
77448681280780593961…64012461639074037761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.548 × 10¹⁰¹(102-digit number)
15489736256156118792…28024923278148075521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.097 × 10¹⁰¹(102-digit number)
30979472512312237584…56049846556296151041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.195 × 10¹⁰¹(102-digit number)
61958945024624475169…12099693112592302081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.239 × 10¹⁰²(103-digit number)
12391789004924895033…24199386225184604161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.478 × 10¹⁰²(103-digit number)
24783578009849790067…48398772450369208321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.956 × 10¹⁰²(103-digit number)
49567156019699580135…96797544900738416641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.913 × 10¹⁰²(103-digit number)
99134312039399160270…93595089801476833281
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:57,764,734 XPM·at block #6,815,080 · updates every 60s
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