Block #1,424,260

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2016, 8:03:58 PM · Difficulty 10.7741 · 5,415,058 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee5d497c6f797d63171506cf6bff8286fc5aab09be7e6f63bcec527efec18fc0

Height

#1,424,260

Difficulty

10.774086

Transactions

2

Size

802 B

Version

2

Bits

0ac62a7e

Nonce

25,833,541

Timestamp

1/22/2016, 8:03:58 PM

Confirmations

5,415,058

Merkle Root

7e4c24f72030168f9431a39ae0369e3969b373434c6958a3c702af3a5b1db9fe
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.

5.370 × 10⁹⁶(97-digit number)
53704181295401260899…69601981552001228801
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
5.370 × 10⁹⁶(97-digit number)
53704181295401260899…69601981552001228801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.074 × 10⁹⁷(98-digit number)
10740836259080252179…39203963104002457601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.148 × 10⁹⁷(98-digit number)
21481672518160504359…78407926208004915201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.296 × 10⁹⁷(98-digit number)
42963345036321008719…56815852416009830401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.592 × 10⁹⁷(98-digit number)
85926690072642017439…13631704832019660801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.718 × 10⁹⁸(99-digit number)
17185338014528403487…27263409664039321601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.437 × 10⁹⁸(99-digit number)
34370676029056806975…54526819328078643201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.874 × 10⁹⁸(99-digit number)
68741352058113613951…09053638656157286401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.374 × 10⁹⁹(100-digit number)
13748270411622722790…18107277312314572801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.749 × 10⁹⁹(100-digit number)
27496540823245445580…36214554624629145601
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:57,958,825 XPM·at block #6,839,317 · updates every 60s
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