Block #2,560,492

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/11/2018, 2:55:01 PM · Difficulty 10.9921 · 4,273,158 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61f91cb6837c9696021e1c257353155bc55495eb0ea5a09aecae9dea4be74349

Height

#2,560,492

Difficulty

10.992128

Transactions

2

Size

538 B

Version

2

Bits

0afdfc1f

Nonce

284,349,006

Timestamp

3/11/2018, 2:55:01 PM

Confirmations

4,273,158

Merkle Root

dcfa6cfcdaac505dc93ae000eef74b51f1f9c3b8d9fe54a01bbacc0ec7f68df8
Transactions (2)
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.

2.814 × 10⁹³(94-digit number)
28146697471803046493…24037024676057527039
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
2.814 × 10⁹³(94-digit number)
28146697471803046493…24037024676057527039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.629 × 10⁹³(94-digit number)
56293394943606092987…48074049352115054079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.125 × 10⁹⁴(95-digit number)
11258678988721218597…96148098704230108159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.251 × 10⁹⁴(95-digit number)
22517357977442437195…92296197408460216319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.503 × 10⁹⁴(95-digit number)
45034715954884874390…84592394816920432639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.006 × 10⁹⁴(95-digit number)
90069431909769748780…69184789633840865279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.801 × 10⁹⁵(96-digit number)
18013886381953949756…38369579267681730559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.602 × 10⁹⁵(96-digit number)
36027772763907899512…76739158535363461119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.205 × 10⁹⁵(96-digit number)
72055545527815799024…53478317070726922239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.441 × 10⁹⁶(97-digit number)
14411109105563159804…06956634141453844479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.882 × 10⁹⁶(97-digit number)
28822218211126319609…13913268282907688959
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,913,414 XPM·at block #6,833,649 · updates every 60s
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