Block #1,421,439

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/20/2016, 4:25:09 PM · Difficulty 10.7861 · 5,389,328 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a78765fa917859f6808ba9c412a637e800d103e7c75fc8fe6c49c14f668187c8

Height

#1,421,439

Difficulty

10.786130

Transactions

2

Size

6.78 KB

Version

2

Bits

0ac93fcc

Nonce

1,635,575,102

Timestamp

1/20/2016, 4:25:09 PM

Confirmations

5,389,328

Merkle Root

4bf05ef8961148096d05e6b9fdd70a152e613c3e6cdf19ee9a92191d080395e5
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.

1.456 × 10⁹⁴(95-digit number)
14564510649235601879…32175864902142112639
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
1.456 × 10⁹⁴(95-digit number)
14564510649235601879…32175864902142112639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.912 × 10⁹⁴(95-digit number)
29129021298471203758…64351729804284225279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.825 × 10⁹⁴(95-digit number)
58258042596942407516…28703459608568450559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.165 × 10⁹⁵(96-digit number)
11651608519388481503…57406919217136901119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.330 × 10⁹⁵(96-digit number)
23303217038776963006…14813838434273802239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.660 × 10⁹⁵(96-digit number)
46606434077553926013…29627676868547604479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.321 × 10⁹⁵(96-digit number)
93212868155107852026…59255353737095208959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.864 × 10⁹⁶(97-digit number)
18642573631021570405…18510707474190417919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.728 × 10⁹⁶(97-digit number)
37285147262043140810…37021414948380835839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.457 × 10⁹⁶(97-digit number)
74570294524086281620…74042829896761671679
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:57,730,231 XPM·at block #6,810,766 · updates every 60s
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