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Block #2,762,082

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 8:23:54 PM Β· Difficulty 11.6549 Β· 4,082,734 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0501da3d0b5c604fa087609e797d571105760cd04590b1f8ae9f972d4e05d6ac
View on Chainz β†—

Height

#2,762,082

Difficulty

11.654878

Transactions

1

Size

200 B

Version

2

Bits

0ba7a614

Nonce

1,791,960,169

Timestamp

7/23/2018, 8:23:54 PM

Confirmations

4,082,734

Mined by

⛏️ P2SHAJduSiscpb2j8uLRFoF2VLJmJW2m8D8MJj

Merkle Root

276156d04fff58af488fdec5dd23e1a2818e2c562b427b32f40ae70396856ac2
Transactions (1)
Coinbase276156d04fff58…0ae70396856ac2
1 in β†’ 1 out7.3500 XPM110 B
AJduSisc…2m8D8MJj
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.

8.209 Γ— 10⁹³(94-digit number)
82091259420448700383…15418554882351785459
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
8.209 Γ— 10⁹³(94-digit number)
82091259420448700383…15418554882351785459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.641 Γ— 10⁹⁴(95-digit number)
16418251884089740076…30837109764703570919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.283 Γ— 10⁹⁴(95-digit number)
32836503768179480153…61674219529407141839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.567 Γ— 10⁹⁴(95-digit number)
65673007536358960306…23348439058814283679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.313 Γ— 10⁹⁡(96-digit number)
13134601507271792061…46696878117628567359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.626 Γ— 10⁹⁡(96-digit number)
26269203014543584122…93393756235257134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.253 Γ— 10⁹⁡(96-digit number)
52538406029087168245…86787512470514269439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.050 Γ— 10⁹⁢(97-digit number)
10507681205817433649…73575024941028538879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.101 Γ— 10⁹⁢(97-digit number)
21015362411634867298…47150049882057077759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.203 Γ— 10⁹⁢(97-digit number)
42030724823269734596…94300099764114155519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.406 Γ— 10⁹⁢(97-digit number)
84061449646539469192…88600199528228311039
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:58,002,935 XPMΒ·at block #6,844,815 Β· updates every 60s
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