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Block #1,482,216

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/3/2016, 6:33:18 PM Β· Difficulty 10.7273 Β· 5,360,598 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
50ca176a2a00bbfd44d0239a98c9afa731fc534884e1b7c315fdd838494107ed
View on Chainz β†—

Height

#1,482,216

Difficulty

10.727337

Transactions

1

Size

200 B

Version

2

Bits

0aba32c3

Nonce

683,063,502

Timestamp

3/3/2016, 6:33:18 PM

Confirmations

5,360,598

Mined by

⛏️ P2SHAHbozw9KvTXm8pXDjJCCmPzfhWYKDKWcGz

Merkle Root

bbd2b16dd26d7e7b7fa5a7998318e36d1ab0548dd411848bcc8e8dd1e1e42fd8
Transactions (1)
Coinbasebbd2b16dd26d7e…8e8dd1e1e42fd8
1 in β†’ 1 out8.6800 XPM110 B
AHbozw9K…YKDKWcGz
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.

1.274 Γ— 10⁹⁡(96-digit number)
12745401451462978621…32696626280680801279
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
1.274 Γ— 10⁹⁡(96-digit number)
12745401451462978621…32696626280680801279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.549 Γ— 10⁹⁡(96-digit number)
25490802902925957242…65393252561361602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.098 Γ— 10⁹⁡(96-digit number)
50981605805851914485…30786505122723205119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁢(97-digit number)
10196321161170382897…61573010245446410239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.039 Γ— 10⁹⁢(97-digit number)
20392642322340765794…23146020490892820479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.078 Γ— 10⁹⁢(97-digit number)
40785284644681531588…46292040981785640959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.157 Γ— 10⁹⁢(97-digit number)
81570569289363063177…92584081963571281919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.631 Γ— 10⁹⁷(98-digit number)
16314113857872612635…85168163927142563839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.262 Γ— 10⁹⁷(98-digit number)
32628227715745225270…70336327854285127679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.525 Γ— 10⁹⁷(98-digit number)
65256455431490450541…40672655708570255359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁸(99-digit number)
13051291086298090108…81345311417140510719
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:57,986,852 XPMΒ·at block #6,842,813 Β· updates every 60s
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