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Block #2,817,986

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2018, 5:54:18 AM Β· Difficulty 11.6964 Β· 4,021,830 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c0e10289ad0a923b1911e0933c4f35f8d4fa305286738f1ad511c525ae28a44
View on Chainz β†—

Height

#2,817,986

Difficulty

11.696416

Transactions

1

Size

198 B

Version

2

Bits

0bb2484b

Nonce

242,124,738

Timestamp

8/31/2018, 5:54:18 AM

Confirmations

4,021,830

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

49cf42eff91ec621156682c129ece311992b2bd2b7e94f2c8e6a79f81bdab3a8
Transactions (1)
Coinbase49cf42eff91ec6…6a79f81bdab3a8
1 in β†’ 1 out7.3000 XPM109 B
AZtxQr2F…7grUWrUz
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.

3.313 Γ— 10⁹²(93-digit number)
33135013616491180765…37490638147375673599
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
3.313 Γ— 10⁹²(93-digit number)
33135013616491180765…37490638147375673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.627 Γ— 10⁹²(93-digit number)
66270027232982361530…74981276294751347199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.325 Γ— 10⁹³(94-digit number)
13254005446596472306…49962552589502694399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.650 Γ— 10⁹³(94-digit number)
26508010893192944612…99925105179005388799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.301 Γ— 10⁹³(94-digit number)
53016021786385889224…99850210358010777599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.060 Γ— 10⁹⁴(95-digit number)
10603204357277177844…99700420716021555199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.120 Γ— 10⁹⁴(95-digit number)
21206408714554355689…99400841432043110399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.241 Γ— 10⁹⁴(95-digit number)
42412817429108711379…98801682864086220799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.482 Γ— 10⁹⁴(95-digit number)
84825634858217422758…97603365728172441599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.696 Γ— 10⁹⁡(96-digit number)
16965126971643484551…95206731456344883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.393 Γ— 10⁹⁡(96-digit number)
33930253943286969103…90413462912689766399
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:57,962,822 XPMΒ·at block #6,839,815 Β· updates every 60s
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