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Block #2,633,800

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 2:59:12 PM Β· Difficulty 11.2087 Β· 4,204,340 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5648b7c4c5cbdcebb9b0976542d369308b28b34d15d367ee0500ab5f9b8326e7
View on Chainz β†—

Height

#2,633,800

Difficulty

11.208673

Transactions

1

Size

200 B

Version

2

Bits

0b356b9e

Nonce

1,151,831,130

Timestamp

4/28/2018, 2:59:12 PM

Confirmations

4,204,340

Mined by

⛏️ P2SHAdR8qwqtdcU6qaDGdfb49uzWsFrcZesXsL

Merkle Root

16c0133d96f0f7f6cabcfb8dbcb3bbb17a0c91100aac4a7b73a4562ba0be759c
Transactions (1)
Coinbase16c0133d96f0f7…a4562ba0be759c
1 in β†’ 1 out7.9500 XPM110 B
AdR8qwqt…rcZesXsL
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.

1.189 Γ— 10⁹⁴(95-digit number)
11895342869732321705…78900289710091243519
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
1.189 Γ— 10⁹⁴(95-digit number)
11895342869732321705…78900289710091243519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.379 Γ— 10⁹⁴(95-digit number)
23790685739464643411…57800579420182487039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.758 Γ— 10⁹⁴(95-digit number)
47581371478929286822…15601158840364974079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.516 Γ— 10⁹⁴(95-digit number)
95162742957858573645…31202317680729948159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁡(96-digit number)
19032548591571714729…62404635361459896319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.806 Γ— 10⁹⁡(96-digit number)
38065097183143429458…24809270722919792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.613 Γ— 10⁹⁡(96-digit number)
76130194366286858916…49618541445839585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁢(97-digit number)
15226038873257371783…99237082891679170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.045 Γ— 10⁹⁢(97-digit number)
30452077746514743566…98474165783358341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.090 Γ— 10⁹⁢(97-digit number)
60904155493029487133…96948331566716682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁷(98-digit number)
12180831098605897426…93896663133433364479
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:57,949,388 XPMΒ·at block #6,838,139 Β· updates every 60s
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