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Block #1,162,003

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2015, 2:23:13 AM Β· Difficulty 10.9361 Β· 5,652,013 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e76c8e8b3ff2ca0642bf86fe87584eb60601f3528ef19547e58805c61f5a9e02
View on Chainz β†—

Height

#1,162,003

Difficulty

10.936059

Transactions

2

Size

3.02 KB

Version

2

Bits

0aefa191

Nonce

229,783,865

Timestamp

7/20/2015, 2:23:13 AM

Confirmations

5,652,013

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

ae6e5e6bd745044161094c26beafe322ce983b63c7b31f88e53c715f7c9b0058
Transactions (2)
Coinbase79aeff8e586981…4fa28b001e80ea
1 in β†’ 1 out8.3800 XPM116 B
AJCEY9yy…tg97E6zm
d9cde22835fed3…f136e4d6d52acc
19 in β†’ 2 out3.0100 XPM2.82 KB
AQx4ZNLa…ZdG7Zj3MAL2Dq1uM…Smbo4eKw
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.

3.070 Γ— 10⁹⁢(97-digit number)
30709216504085649866…25740132133936249279
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
3.070 Γ— 10⁹⁢(97-digit number)
30709216504085649866…25740132133936249279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.141 Γ— 10⁹⁢(97-digit number)
61418433008171299732…51480264267872498559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.228 Γ— 10⁹⁷(98-digit number)
12283686601634259946…02960528535744997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.456 Γ— 10⁹⁷(98-digit number)
24567373203268519892…05921057071489994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.913 Γ— 10⁹⁷(98-digit number)
49134746406537039785…11842114142979988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.826 Γ— 10⁹⁷(98-digit number)
98269492813074079571…23684228285959976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.965 Γ— 10⁹⁸(99-digit number)
19653898562614815914…47368456571919953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.930 Γ— 10⁹⁸(99-digit number)
39307797125229631828…94736913143839907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.861 Γ— 10⁹⁸(99-digit number)
78615594250459263657…89473826287679815679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.572 Γ— 10⁹⁹(100-digit number)
15723118850091852731…78947652575359631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.144 Γ— 10⁹⁹(100-digit number)
31446237700183705462…57895305150719262719
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:57,756,212 XPMΒ·at block #6,814,015 Β· updates every 60s
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