Block #1,198,903

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/18/2015, 10:16:13 AM · Difficulty 10.8183 · 5,607,014 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f2054ce4df46644c18a11972b461ecd185a213890c08e461fdae52b4677a286

Height

#1,198,903

Difficulty

10.818259

Transactions

3

Size

652 B

Version

2

Bits

0ad17968

Nonce

1,574,374,026

Timestamp

8/18/2015, 10:16:13 AM

Confirmations

5,607,014

Merkle Root

411e360d8b806952b9955f3f0c571812bea277a547d96bd868cca890dcce2a85
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.

8.035 × 10⁹²(93-digit number)
80358127434774267825…17913349448753389201
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
8.035 × 10⁹²(93-digit number)
80358127434774267825…17913349448753389201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.607 × 10⁹³(94-digit number)
16071625486954853565…35826698897506778401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.214 × 10⁹³(94-digit number)
32143250973909707130…71653397795013556801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.428 × 10⁹³(94-digit number)
64286501947819414260…43306795590027113601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.285 × 10⁹⁴(95-digit number)
12857300389563882852…86613591180054227201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.571 × 10⁹⁴(95-digit number)
25714600779127765704…73227182360108454401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.142 × 10⁹⁴(95-digit number)
51429201558255531408…46454364720216908801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.028 × 10⁹⁵(96-digit number)
10285840311651106281…92908729440433817601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.057 × 10⁹⁵(96-digit number)
20571680623302212563…85817458880867635201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.114 × 10⁹⁵(96-digit number)
41143361246604425126…71634917761735270401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.228 × 10⁹⁵(96-digit number)
82286722493208850253…43269835523470540801
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:57,691,426 XPM·at block #6,805,916 · updates every 60s
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