Block #367,806

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/20/2014, 8:10:09 AM · Difficulty 10.4356 · 6,448,412 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eb93ea082c748b8cea522bff2334a8f5e4137101acbef4e069f23fcc4c01e6a6

Height

#367,806

Difficulty

10.435639

Transactions

1

Size

1007 B

Version

2

Bits

0a6f8604

Nonce

85,355

Timestamp

1/20/2014, 8:10:09 AM

Confirmations

6,448,412

Merkle Root

e9f0479d15ef1ae1694a83f2cbbd43e2f5710cf688251a4113c05221a64849ef
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.

5.066 × 10¹⁰⁴(105-digit number)
50664539970859471045…06129916638229075679
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
5.066 × 10¹⁰⁴(105-digit number)
50664539970859471045…06129916638229075679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.013 × 10¹⁰⁵(106-digit number)
10132907994171894209…12259833276458151359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.026 × 10¹⁰⁵(106-digit number)
20265815988343788418…24519666552916302719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.053 × 10¹⁰⁵(106-digit number)
40531631976687576836…49039333105832605439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.106 × 10¹⁰⁵(106-digit number)
81063263953375153672…98078666211665210879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.621 × 10¹⁰⁶(107-digit number)
16212652790675030734…96157332423330421759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.242 × 10¹⁰⁶(107-digit number)
32425305581350061468…92314664846660843519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.485 × 10¹⁰⁶(107-digit number)
64850611162700122937…84629329693321687039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.297 × 10¹⁰⁷(108-digit number)
12970122232540024587…69258659386643374079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.594 × 10¹⁰⁷(108-digit number)
25940244465080049175…38517318773286748159
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:57,773,873 XPM·at block #6,816,217 · updates every 60s
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