Block #572,953

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/2/2014, 10:38:17 AM · Difficulty 10.9663 · 6,241,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b9d33cbd12bef6032dc931f4c3146b68000d8bf864364cfbba7d0b540fa6fcac

Height

#572,953

Difficulty

10.966341

Transactions

2

Size

576 B

Version

2

Bits

0af76223

Nonce

23,493

Timestamp

6/2/2014, 10:38:17 AM

Confirmations

6,241,141

Merkle Root

e444aac10a21fbc25ce62563e1b6d502146d7591907d82d81a12d9b24cf31e0e
Transactions (2)
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.

9.167 × 10¹⁰⁰(101-digit number)
91678133386192911226…69756644606376871199
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
9.167 × 10¹⁰⁰(101-digit number)
91678133386192911226…69756644606376871199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.833 × 10¹⁰¹(102-digit number)
18335626677238582245…39513289212753742399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.667 × 10¹⁰¹(102-digit number)
36671253354477164490…79026578425507484799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.334 × 10¹⁰¹(102-digit number)
73342506708954328981…58053156851014969599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.466 × 10¹⁰²(103-digit number)
14668501341790865796…16106313702029939199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.933 × 10¹⁰²(103-digit number)
29337002683581731592…32212627404059878399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.867 × 10¹⁰²(103-digit number)
58674005367163463184…64425254808119756799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.173 × 10¹⁰³(104-digit number)
11734801073432692636…28850509616239513599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.346 × 10¹⁰³(104-digit number)
23469602146865385273…57701019232479027199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.693 × 10¹⁰³(104-digit number)
46939204293730770547…15402038464958054399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.387 × 10¹⁰³(104-digit number)
93878408587461541095…30804076929916108799
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:57,756,834 XPM·at block #6,814,093 · updates every 60s
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