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Block #2,643,268

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 1:15:20 AM Β· Difficulty 11.6782 Β· 4,193,805 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4f4d1f0f53f3128571c0fa0fac64b87c88c73a78b32e3373946784910fba7a2a
View on Chainz β†—

Height

#2,643,268

Difficulty

11.678208

Transactions

1

Size

201 B

Version

2

Bits

0bad9f05

Nonce

596,631,573

Timestamp

5/2/2018, 1:15:20 AM

Confirmations

4,193,805

Mined by

⛏️ P2SHAJ3t93FHGQjxnkbdUfBWYw4iPNXt1wpEox

Merkle Root

9236ce9d0513b6512fb7476fe899973a60493409483c230f07fe19e203b3342b
Transactions (1)
Coinbase9236ce9d0513b6…fe19e203b3342b
1 in β†’ 1 out7.3200 XPM110 B
AJ3t93FH…Xt1wpEox
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.

1.798 Γ— 10⁹⁢(97-digit number)
17982540567169111608…37090782949337425919
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
1.798 Γ— 10⁹⁢(97-digit number)
17982540567169111608…37090782949337425919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.596 Γ— 10⁹⁢(97-digit number)
35965081134338223216…74181565898674851839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.193 Γ— 10⁹⁢(97-digit number)
71930162268676446432…48363131797349703679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.438 Γ— 10⁹⁷(98-digit number)
14386032453735289286…96726263594699407359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.877 Γ— 10⁹⁷(98-digit number)
28772064907470578572…93452527189398814719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.754 Γ— 10⁹⁷(98-digit number)
57544129814941157145…86905054378797629439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁸(99-digit number)
11508825962988231429…73810108757595258879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.301 Γ— 10⁹⁸(99-digit number)
23017651925976462858…47620217515190517759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.603 Γ— 10⁹⁸(99-digit number)
46035303851952925716…95240435030381035519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.207 Γ— 10⁹⁸(99-digit number)
92070607703905851433…90480870060762071039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁹(100-digit number)
18414121540781170286…80961740121524142079
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:57,940,889 XPMΒ·at block #6,837,072 Β· updates every 60s
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