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Block #2,850,469

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2018, 9:59:16 AM Β· Difficulty 11.7291 Β· 3,993,362 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a32a102ffad2e1180f935f10b438c481bc01fa3a0a9d50019a649afe1d5a35e
View on Chainz β†—

Height

#2,850,469

Difficulty

11.729148

Transactions

1

Size

201 B

Version

2

Bits

0bbaa973

Nonce

2,090,682,961

Timestamp

9/22/2018, 9:59:16 AM

Confirmations

3,993,362

Mined by

⛏️ P2SHAQXvbRbcpUaaw6eAzoa76iMgv8yyY6yMap

Merkle Root

b9cf37f43c62892abe853f2c8221bba4b7d3ef80066672f32cd0831f85742be6
Transactions (1)
Coinbaseb9cf37f43c6289…d0831f85742be6
1 in β†’ 1 out7.2600 XPM110 B
AQXvbRbc…yyY6yMap
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.

7.807 Γ— 10⁹⁷(98-digit number)
78074278937481381134…16911110755297484799
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
7.807 Γ— 10⁹⁷(98-digit number)
78074278937481381134…16911110755297484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁸(99-digit number)
15614855787496276226…33822221510594969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.122 Γ— 10⁹⁸(99-digit number)
31229711574992552453…67644443021189939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.245 Γ— 10⁹⁸(99-digit number)
62459423149985104907…35288886042379878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.249 Γ— 10⁹⁹(100-digit number)
12491884629997020981…70577772084759756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.498 Γ— 10⁹⁹(100-digit number)
24983769259994041963…41155544169519513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.996 Γ— 10⁹⁹(100-digit number)
49967538519988083926…82311088339039027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.993 Γ— 10⁹⁹(100-digit number)
99935077039976167852…64622176678078054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.998 Γ— 10¹⁰⁰(101-digit number)
19987015407995233570…29244353356156108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.997 Γ— 10¹⁰⁰(101-digit number)
39974030815990467140…58488706712312217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.994 Γ— 10¹⁰⁰(101-digit number)
79948061631980934281…16977413424624435199
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:57,995,024 XPMΒ·at block #6,843,830 Β· updates every 60s
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