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Block #623,384

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/8/2014, 11:54:43 AM Β· Difficulty 10.9562 Β· 6,192,834 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc3b2a593fad865ff064af2ccbdef7deada3c44d2e0b58740adf24b450f948e9
View on Chainz β†—

Height

#623,384

Difficulty

10.956181

Transactions

2

Size

434 B

Version

2

Bits

0af4c84b

Nonce

564,763,624

Timestamp

7/8/2014, 11:54:43 AM

Confirmations

6,192,834

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a225f8909218e15c1003925682978d2de4d5fd83daa459969c3b4dcf564ab836
Transactions (2)
Coinbased96ee747e32bb5…b042cf71a0f214
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
801266b2bcbf32…d6859d66a25612
1 in β†’ 2 out8.3200 XPM227 B
AGgdQTy7…7D2enSpzAZ4AUUAY…wt3vRLWV
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.

2.646 Γ— 10⁹⁷(98-digit number)
26468433018098338905…59905297318278127199
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
2.646 Γ— 10⁹⁷(98-digit number)
26468433018098338905…59905297318278127199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.293 Γ— 10⁹⁷(98-digit number)
52936866036196677810…19810594636556254399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁸(99-digit number)
10587373207239335562…39621189273112508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.117 Γ— 10⁹⁸(99-digit number)
21174746414478671124…79242378546225017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.234 Γ— 10⁹⁸(99-digit number)
42349492828957342248…58484757092450035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.469 Γ— 10⁹⁸(99-digit number)
84698985657914684496…16969514184900070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.693 Γ— 10⁹⁹(100-digit number)
16939797131582936899…33939028369800140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.387 Γ— 10⁹⁹(100-digit number)
33879594263165873798…67878056739600281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.775 Γ— 10⁹⁹(100-digit number)
67759188526331747596…35756113479200563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.355 Γ— 10¹⁰⁰(101-digit number)
13551837705266349519…71512226958401126399
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:57,773,873 XPMΒ·at block #6,816,217 Β· updates every 60s
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