Block #371,769

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2014, 3:33:26 AM · Difficulty 10.4273 · 6,465,110 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cba17bd701701c6108c841282bd90b5049ef7908e87b804a8a6aac3659107bfb

Height

#371,769

Difficulty

10.427270

Transactions

4

Size

1.58 KB

Version

2

Bits

0a6d6194

Nonce

2,442

Timestamp

1/23/2014, 3:33:26 AM

Confirmations

6,465,110

Merkle Root

15d34ea55aab6f62dcec8a8fd0d9273eb8ce4253e3af3ef2570f9b96503a055d
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.

8.750 × 10⁹⁷(98-digit number)
87503682032555160038…27091081642507012639
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
8.750 × 10⁹⁷(98-digit number)
87503682032555160038…27091081642507012639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.750 × 10⁹⁸(99-digit number)
17500736406511032007…54182163285014025279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.500 × 10⁹⁸(99-digit number)
35001472813022064015…08364326570028050559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.000 × 10⁹⁸(99-digit number)
70002945626044128030…16728653140056101119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.400 × 10⁹⁹(100-digit number)
14000589125208825606…33457306280112202239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.800 × 10⁹⁹(100-digit number)
28001178250417651212…66914612560224404479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.600 × 10⁹⁹(100-digit number)
56002356500835302424…33829225120448808959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.120 × 10¹⁰⁰(101-digit number)
11200471300167060484…67658450240897617919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.240 × 10¹⁰⁰(101-digit number)
22400942600334120969…35316900481795235839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.480 × 10¹⁰⁰(101-digit number)
44801885200668241939…70633800963590471679
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:57,939,323 XPM·at block #6,836,878 · updates every 60s
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