Block #2,524,688

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/17/2018, 2:22:00 AM · Difficulty 10.9832 · 4,315,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f53163d88964e161cafe82349df2373c02052844ec716fcb3884a9d4b1dc8d91

Height

#2,524,688

Difficulty

10.983181

Transactions

4

Size

1.15 KB

Version

2

Bits

0afbb1b9

Nonce

258,844,395

Timestamp

2/17/2018, 2:22:00 AM

Confirmations

4,315,855

Merkle Root

1bdea08d5321daac907f75a0bebbc4802438eb2761be3939a8bfa14bf24e8212
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.

4.020 × 10⁹⁵(96-digit number)
40207538305493129862…53162892863045786559
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
4.020 × 10⁹⁵(96-digit number)
40207538305493129862…53162892863045786559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.041 × 10⁹⁵(96-digit number)
80415076610986259725…06325785726091573119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.608 × 10⁹⁶(97-digit number)
16083015322197251945…12651571452183146239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.216 × 10⁹⁶(97-digit number)
32166030644394503890…25303142904366292479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.433 × 10⁹⁶(97-digit number)
64332061288789007780…50606285808732584959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.286 × 10⁹⁷(98-digit number)
12866412257757801556…01212571617465169919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.573 × 10⁹⁷(98-digit number)
25732824515515603112…02425143234930339839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.146 × 10⁹⁷(98-digit number)
51465649031031206224…04850286469860679679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.029 × 10⁹⁸(99-digit number)
10293129806206241244…09700572939721359359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.058 × 10⁹⁸(99-digit number)
20586259612412482489…19401145879442718719
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,968,676 XPM·at block #6,840,542 · updates every 60s
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