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Block #2,638,600

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 8:23:14 AM Β· Difficulty 11.5004 Β· 4,198,155 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75962b667174da2e9a664806668a84a548482a83d6d46100054efe009a10619f
View on Chainz β†—

Height

#2,638,600

Difficulty

11.500355

Transactions

1

Size

200 B

Version

2

Bits

0b80174a

Nonce

155,394,439

Timestamp

4/30/2018, 8:23:14 AM

Confirmations

4,198,155

Mined by

⛏️ P2SHAdkzoeXA3hRv4NRe2CNG2fdrm14GFRhQSp

Merkle Root

e64058dd65cfed63f6345b7d3b05ed6de1a833c1bee488f7dd1a24f125252d79
Transactions (1)
Coinbasee64058dd65cfed…1a24f125252d79
1 in β†’ 1 out7.5500 XPM110 B
AdkzoeXA…4GFRhQSp
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.

3.233 Γ— 10⁹³(94-digit number)
32335399569741804503…43186826054408978919
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
3.233 Γ— 10⁹³(94-digit number)
32335399569741804503…43186826054408978919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.467 Γ— 10⁹³(94-digit number)
64670799139483609006…86373652108817957839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.293 Γ— 10⁹⁴(95-digit number)
12934159827896721801…72747304217635915679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.586 Γ— 10⁹⁴(95-digit number)
25868319655793443602…45494608435271831359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.173 Γ— 10⁹⁴(95-digit number)
51736639311586887205…90989216870543662719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.034 Γ— 10⁹⁡(96-digit number)
10347327862317377441…81978433741087325439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.069 Γ— 10⁹⁡(96-digit number)
20694655724634754882…63956867482174650879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.138 Γ— 10⁹⁡(96-digit number)
41389311449269509764…27913734964349301759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.277 Γ— 10⁹⁡(96-digit number)
82778622898539019528…55827469928698603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.655 Γ— 10⁹⁢(97-digit number)
16555724579707803905…11654939857397207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.311 Γ— 10⁹⁢(97-digit number)
33111449159415607811…23309879714794414079
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,938,327 XPMΒ·at block #6,836,754 Β· updates every 60s
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