Block #1,336,064

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/21/2015, 8:05:52 PM · Difficulty 10.8146 · 5,481,810 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
938491abdd85ecd426730b7bdeedc764f2e89954dec3e4f41bcf271a2d43fdae

Height

#1,336,064

Difficulty

10.814572

Transactions

2

Size

1.18 KB

Version

2

Bits

0ad087d2

Nonce

80,400,837

Timestamp

11/21/2015, 8:05:52 PM

Confirmations

5,481,810

Merkle Root

f99494c2033315d133fa532039db6f48ae9ff878c5698a257643262cd16c2467
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.

9.351 × 10⁹²(93-digit number)
93513091838648889231…32331613421757097599
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
9.351 × 10⁹²(93-digit number)
93513091838648889231…32331613421757097599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.870 × 10⁹³(94-digit number)
18702618367729777846…64663226843514195199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.740 × 10⁹³(94-digit number)
37405236735459555692…29326453687028390399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.481 × 10⁹³(94-digit number)
74810473470919111385…58652907374056780799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.496 × 10⁹⁴(95-digit number)
14962094694183822277…17305814748113561599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.992 × 10⁹⁴(95-digit number)
29924189388367644554…34611629496227123199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.984 × 10⁹⁴(95-digit number)
59848378776735289108…69223258992454246399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.196 × 10⁹⁵(96-digit number)
11969675755347057821…38446517984908492799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.393 × 10⁹⁵(96-digit number)
23939351510694115643…76893035969816985599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.787 × 10⁹⁵(96-digit number)
47878703021388231286…53786071939633971199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.575 × 10⁹⁵(96-digit number)
95757406042776462573…07572143879267942399
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,787,051 XPM·at block #6,817,873 · updates every 60s
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