Block #376,506

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2014, 11:06:29 AM · Difficulty 10.4245 · 6,427,561 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ebd28b2a4eed1f4aa34a8b2ae2c5540175685fbc7de4016e0f614174f2a788c0

Height

#376,506

Difficulty

10.424531

Transactions

3

Size

658 B

Version

2

Bits

0a6cae09

Nonce

11,412

Timestamp

1/26/2014, 11:06:29 AM

Confirmations

6,427,561

Merkle Root

538aee195b98339a2ae481e8a1a016ffe1a1977481747be9284afac1bc7a33ab
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.

3.641 × 10⁹⁷(98-digit number)
36416782219300654667…04098641327109723399
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
3.641 × 10⁹⁷(98-digit number)
36416782219300654667…04098641327109723399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.283 × 10⁹⁷(98-digit number)
72833564438601309335…08197282654219446799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.456 × 10⁹⁸(99-digit number)
14566712887720261867…16394565308438893599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.913 × 10⁹⁸(99-digit number)
29133425775440523734…32789130616877787199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.826 × 10⁹⁸(99-digit number)
58266851550881047468…65578261233755574399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.165 × 10⁹⁹(100-digit number)
11653370310176209493…31156522467511148799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.330 × 10⁹⁹(100-digit number)
23306740620352418987…62313044935022297599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.661 × 10⁹⁹(100-digit number)
46613481240704837974…24626089870044595199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.322 × 10⁹⁹(100-digit number)
93226962481409675949…49252179740089190399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.864 × 10¹⁰⁰(101-digit number)
18645392496281935189…98504359480178380799
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:57,676,593 XPM·at block #6,804,066 · updates every 60s
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