Block #507,067

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2014, 12:09:49 PM · Difficulty 10.8153 · 6,300,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b0957678396cdd7d6a6fe6214101bd25df865b85ae2027e41c406282585b4c5e

Height

#507,067

Difficulty

10.815259

Transactions

5

Size

28.85 KB

Version

2

Bits

0ad0b4d2

Nonce

3,252,778

Timestamp

4/23/2014, 12:09:49 PM

Confirmations

6,300,630

Merkle Root

25c756c0f743bbd5fa655ecb955861d96cf023db2a8db6529a2de6cf22f0be7c
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.

1.433 × 10¹⁰⁰(101-digit number)
14338905760854927957…19190991492781510401
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
1.433 × 10¹⁰⁰(101-digit number)
14338905760854927957…19190991492781510401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.867 × 10¹⁰⁰(101-digit number)
28677811521709855914…38381982985563020801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.735 × 10¹⁰⁰(101-digit number)
57355623043419711828…76763965971126041601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.147 × 10¹⁰¹(102-digit number)
11471124608683942365…53527931942252083201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.294 × 10¹⁰¹(102-digit number)
22942249217367884731…07055863884504166401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.588 × 10¹⁰¹(102-digit number)
45884498434735769462…14111727769008332801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.176 × 10¹⁰¹(102-digit number)
91768996869471538925…28223455538016665601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.835 × 10¹⁰²(103-digit number)
18353799373894307785…56446911076033331201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.670 × 10¹⁰²(103-digit number)
36707598747788615570…12893822152066662401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.341 × 10¹⁰²(103-digit number)
73415197495577231140…25787644304133324801
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:57,705,606 XPM·at block #6,807,696 · updates every 60s
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