Block #2,275,660

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/31/2017, 2:16:58 AM · Difficulty 10.9550 · 4,558,130 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d1b29132b4e71ab646e156d2790c4df69ef48e997f99a76a156642d22cceeec8

Height

#2,275,660

Difficulty

10.955029

Transactions

2

Size

425 B

Version

2

Bits

0af47cc4

Nonce

1,531,162,684

Timestamp

8/31/2017, 2:16:58 AM

Confirmations

4,558,130

Merkle Root

34a60afefa269fc4e287401eead6daf37d67b92d26c90a9aab9c5821901400e8
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.

2.863 × 10⁹²(93-digit number)
28632531845591910600…13750947018164094079
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
2.863 × 10⁹²(93-digit number)
28632531845591910600…13750947018164094079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.726 × 10⁹²(93-digit number)
57265063691183821201…27501894036328188159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.145 × 10⁹³(94-digit number)
11453012738236764240…55003788072656376319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.290 × 10⁹³(94-digit number)
22906025476473528480…10007576145312752639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.581 × 10⁹³(94-digit number)
45812050952947056961…20015152290625505279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.162 × 10⁹³(94-digit number)
91624101905894113922…40030304581251010559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.832 × 10⁹⁴(95-digit number)
18324820381178822784…80060609162502021119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.664 × 10⁹⁴(95-digit number)
36649640762357645568…60121218325004042239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.329 × 10⁹⁴(95-digit number)
73299281524715291137…20242436650008084479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.465 × 10⁹⁵(96-digit number)
14659856304943058227…40484873300016168959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.931 × 10⁹⁵(96-digit number)
29319712609886116455…80969746600032337919
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:57,914,540 XPM·at block #6,833,789 · updates every 60s
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