Block #522,424

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2014, 12:56:06 AM · Difficulty 10.8670 · 6,271,999 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f56374e654bbcbed7f40f92441e4b06958aa4c035f797fbd0939630a804a144d

Height

#522,424

Difficulty

10.867009

Transactions

2

Size

610 B

Version

2

Bits

0addf44d

Nonce

369,888,666

Timestamp

5/3/2014, 12:56:06 AM

Confirmations

6,271,999

Merkle Root

cd0ddfd3280775b57fa46d681bc81a7bff8797b0304c699b42fa83cf938dcc20
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.

2.273 × 10⁹⁹(100-digit number)
22736598574348270805…75648618365631239681
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
2.273 × 10⁹⁹(100-digit number)
22736598574348270805…75648618365631239681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.547 × 10⁹⁹(100-digit number)
45473197148696541611…51297236731262479361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.094 × 10⁹⁹(100-digit number)
90946394297393083223…02594473462524958721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.818 × 10¹⁰⁰(101-digit number)
18189278859478616644…05188946925049917441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.637 × 10¹⁰⁰(101-digit number)
36378557718957233289…10377893850099834881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.275 × 10¹⁰⁰(101-digit number)
72757115437914466579…20755787700199669761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.455 × 10¹⁰¹(102-digit number)
14551423087582893315…41511575400399339521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.910 × 10¹⁰¹(102-digit number)
29102846175165786631…83023150800798679041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.820 × 10¹⁰¹(102-digit number)
58205692350331573263…66046301601597358081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.164 × 10¹⁰²(103-digit number)
11641138470066314652…32092603203194716161
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,599,419 XPM·at block #6,794,422 · updates every 60s
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