Block #930,380

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/10/2015, 12:15:37 PM · Difficulty 10.9024 · 5,870,257 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c623b515709457ec8a3eee79f17dcde0052521854acba025e386044b8c95d962

Height

#930,380

Difficulty

10.902436

Transactions

5

Size

977 B

Version

2

Bits

0ae7060a

Nonce

1,416,975,174

Timestamp

2/10/2015, 12:15:37 PM

Confirmations

5,870,257

Merkle Root

30a9ccf79725bb3525ce09539bdd8f3dd7d6b85be29c1d72e08b616e36b910bb
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.

4.385 × 10⁹⁷(98-digit number)
43852804149310339155…81131800549432033279
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
4.385 × 10⁹⁷(98-digit number)
43852804149310339155…81131800549432033279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.770 × 10⁹⁷(98-digit number)
87705608298620678310…62263601098864066559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.754 × 10⁹⁸(99-digit number)
17541121659724135662…24527202197728133119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.508 × 10⁹⁸(99-digit number)
35082243319448271324…49054404395456266239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.016 × 10⁹⁸(99-digit number)
70164486638896542648…98108808790912532479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.403 × 10⁹⁹(100-digit number)
14032897327779308529…96217617581825064959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.806 × 10⁹⁹(100-digit number)
28065794655558617059…92435235163650129919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.613 × 10⁹⁹(100-digit number)
56131589311117234118…84870470327300259839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.122 × 10¹⁰⁰(101-digit number)
11226317862223446823…69740940654600519679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.245 × 10¹⁰⁰(101-digit number)
22452635724446893647…39481881309201039359
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:57,649,161 XPM·at block #6,800,636 · updates every 60s
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