Block #370,176

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/21/2014, 9:59:30 PM · Difficulty 10.4472 · 6,444,214 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
608b9cf06a8fb563a705e12342244fa7a71d1ce7cd0526de11e00801cbe711cb

Height

#370,176

Difficulty

10.447162

Transactions

4

Size

2.76 KB

Version

2

Bits

0a72792e

Nonce

140,021

Timestamp

1/21/2014, 9:59:30 PM

Confirmations

6,444,214

Merkle Root

cbd3a7ce3a0c047d29e4d01902c81cbcf540e51f719102ae5ef9df13d2cb8c86
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.

4.961 × 10⁹⁹(100-digit number)
49613321377353680980…23574658692374297599
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
4.961 × 10⁹⁹(100-digit number)
49613321377353680980…23574658692374297599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.922 × 10⁹⁹(100-digit number)
99226642754707361961…47149317384748595199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.984 × 10¹⁰⁰(101-digit number)
19845328550941472392…94298634769497190399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.969 × 10¹⁰⁰(101-digit number)
39690657101882944784…88597269538994380799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.938 × 10¹⁰⁰(101-digit number)
79381314203765889569…77194539077988761599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.587 × 10¹⁰¹(102-digit number)
15876262840753177913…54389078155977523199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.175 × 10¹⁰¹(102-digit number)
31752525681506355827…08778156311955046399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.350 × 10¹⁰¹(102-digit number)
63505051363012711655…17556312623910092799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.270 × 10¹⁰²(103-digit number)
12701010272602542331…35112625247820185599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.540 × 10¹⁰²(103-digit number)
25402020545205084662…70225250495640371199
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:57,759,181 XPM·at block #6,814,389 · updates every 60s
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