Block #602,645

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/26/2014, 10:51:13 AM · Difficulty 10.9131 · 6,211,803 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb9a90308186b1a8f598193abfa55a0611c40351f810335c78a9a77b9d20699c

Height

#602,645

Difficulty

10.913108

Transactions

4

Size

886 B

Version

2

Bits

0ae9c175

Nonce

55,986,744

Timestamp

6/26/2014, 10:51:13 AM

Confirmations

6,211,803

Merkle Root

ff95aac98fd6bb1bdfb917b3838256d7a23e468d003f92bd650dc5bd41d89be1
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.

1.938 × 10⁹⁸(99-digit number)
19389312050606834667…23171720258265865921
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
1.938 × 10⁹⁸(99-digit number)
19389312050606834667…23171720258265865921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.877 × 10⁹⁸(99-digit number)
38778624101213669334…46343440516531731841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.755 × 10⁹⁸(99-digit number)
77557248202427338668…92686881033063463681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.551 × 10⁹⁹(100-digit number)
15511449640485467733…85373762066126927361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.102 × 10⁹⁹(100-digit number)
31022899280970935467…70747524132253854721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.204 × 10⁹⁹(100-digit number)
62045798561941870935…41495048264507709441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.240 × 10¹⁰⁰(101-digit number)
12409159712388374187…82990096529015418881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.481 × 10¹⁰⁰(101-digit number)
24818319424776748374…65980193058030837761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.963 × 10¹⁰⁰(101-digit number)
49636638849553496748…31960386116061675521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.927 × 10¹⁰⁰(101-digit number)
99273277699106993496…63920772232123351041
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:57,759,654 XPM·at block #6,814,447 · updates every 60s
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