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Block #1,482,183

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/3/2016, 6:10:48 PM Β· Difficulty 10.7268 Β· 5,344,547 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
051b2a579a931a032e4f4da4de8314ec8332fa38e85f5a7aecdbb4fbe6eefac8
View on Chainz β†—

Height

#1,482,183

Difficulty

10.726781

Transactions

2

Size

4.02 KB

Version

2

Bits

0aba0e4f

Nonce

526,378,341

Timestamp

3/3/2016, 6:10:48 PM

Confirmations

5,344,547

Mined by

⛏️ P2SHASviz1n7VdfwSV4mx8J939CA1q6RjVbF8q

Merkle Root

22fd9e89f8e7679092e51c208d4289f4f0744b39aa1fa375fcffa96ed7b02c07
Transactions (2)
Coinbase3a9018facc6d24…8e8313bbc289e0
1 in β†’ 1 out8.7200 XPM109 B
ASviz1n7…6RjVbF8q
ac72063a2733b3…b8e04be96f839d
26 in β†’ 2 out74.4181 XPM3.83 KB
AHNkwmbJ…EUxEmniYAMnv4Qa1…BkmG2hc3
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.

1.986 Γ— 10⁹⁡(96-digit number)
19865438910737947877…31011932825823538559
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
1.986 Γ— 10⁹⁡(96-digit number)
19865438910737947877…31011932825823538559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.973 Γ— 10⁹⁡(96-digit number)
39730877821475895754…62023865651647077119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.946 Γ— 10⁹⁡(96-digit number)
79461755642951791508…24047731303294154239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.589 Γ— 10⁹⁢(97-digit number)
15892351128590358301…48095462606588308479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.178 Γ— 10⁹⁢(97-digit number)
31784702257180716603…96190925213176616959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.356 Γ— 10⁹⁢(97-digit number)
63569404514361433206…92381850426353233919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁷(98-digit number)
12713880902872286641…84763700852706467839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.542 Γ— 10⁹⁷(98-digit number)
25427761805744573282…69527401705412935679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.085 Γ— 10⁹⁷(98-digit number)
50855523611489146565…39054803410825871359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.017 Γ— 10⁹⁸(99-digit number)
10171104722297829313…78109606821651742719
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:57,857,994 XPMΒ·at block #6,826,729 Β· updates every 60s
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