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Block #824,393

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/23/2014, 1:33:59 PM Β· Difficulty 10.9769 Β· 5,983,064 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d4a1e58dbc82c060da9eec96102016a3c1ab81cbfba722b59653918b6f2a1b1
View on Chainz β†—

Height

#824,393

Difficulty

10.976904

Transactions

2

Size

1.15 KB

Version

2

Bits

0afa1666

Nonce

135,625,072

Timestamp

11/23/2014, 1:33:59 PM

Confirmations

5,983,064

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ad1dd07acea80a18028be385ea14fc274f81abf2fb63f28a239209719c0bf2a3
Transactions (2)
Coinbase1c16ae8619f052…78e3561fbe2c3d
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
01227273a706c4…1839fed34d3387
6 in β†’ 2 out400.0000 XPM969 B
AY6zxofy…SaX3wdQnAcVGsc7g…gPwcKbbK
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.382 Γ— 10⁹⁡(96-digit number)
13823295039388144115…83258420968549021359
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.382 Γ— 10⁹⁡(96-digit number)
13823295039388144115…83258420968549021359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.764 Γ— 10⁹⁡(96-digit number)
27646590078776288231…66516841937098042719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.529 Γ— 10⁹⁡(96-digit number)
55293180157552576462…33033683874196085439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁢(97-digit number)
11058636031510515292…66067367748392170879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.211 Γ— 10⁹⁢(97-digit number)
22117272063021030585…32134735496784341759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.423 Γ— 10⁹⁢(97-digit number)
44234544126042061170…64269470993568683519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.846 Γ— 10⁹⁢(97-digit number)
88469088252084122340…28538941987137367039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.769 Γ— 10⁹⁷(98-digit number)
17693817650416824468…57077883974274734079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.538 Γ— 10⁹⁷(98-digit number)
35387635300833648936…14155767948549468159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.077 Γ— 10⁹⁷(98-digit number)
70775270601667297872…28311535897098936319
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,703,680 XPMΒ·at block #6,807,456 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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