Block #1,205,550

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/23/2015, 1:57:34 PM · Difficulty 10.7884 · 5,599,641 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42bce85d06dbd631f2ed056bed11d697bd01c30edb7bb76931f084762d277872

Height

#1,205,550

Difficulty

10.788369

Transactions

4

Size

1.04 KB

Version

2

Bits

0ac9d286

Nonce

57,852

Timestamp

8/23/2015, 1:57:34 PM

Confirmations

5,599,641

Merkle Root

57a99e10dbca61fc3ac10e1955ea557ab584e36f0510c8756bd2a6f9af647e8c
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.

8.164 × 10⁹⁸(99-digit number)
81645803946737315890…53231099234793511841
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
8.164 × 10⁹⁸(99-digit number)
81645803946737315890…53231099234793511841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.632 × 10⁹⁹(100-digit number)
16329160789347463178…06462198469587023681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.265 × 10⁹⁹(100-digit number)
32658321578694926356…12924396939174047361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.531 × 10⁹⁹(100-digit number)
65316643157389852712…25848793878348094721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.306 × 10¹⁰⁰(101-digit number)
13063328631477970542…51697587756696189441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.612 × 10¹⁰⁰(101-digit number)
26126657262955941084…03395175513392378881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.225 × 10¹⁰⁰(101-digit number)
52253314525911882169…06790351026784757761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.045 × 10¹⁰¹(102-digit number)
10450662905182376433…13580702053569515521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.090 × 10¹⁰¹(102-digit number)
20901325810364752867…27161404107139031041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.180 × 10¹⁰¹(102-digit number)
41802651620729505735…54322808214278062081
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:57,685,599 XPM·at block #6,805,190 · updates every 60s
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