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Block #2,829,044

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2018, 6:09:56 PM Β· Difficulty 11.7109 Β· 4,014,146 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cc26c29ef32152f6a4ccd936adeb232361658a65462498d8100a0e8356653376
View on Chainz β†—

Height

#2,829,044

Difficulty

11.710858

Transactions

1

Size

201 B

Version

2

Bits

0bb5fac9

Nonce

1,812,702,147

Timestamp

9/7/2018, 6:09:56 PM

Confirmations

4,014,146

Mined by

⛏️ P2SHAV6gKZLHV8Nj3cL3vNL8QbXruSHRimzWbc

Merkle Root

9bd84bd53ddf76a3104c776c7e4cfe392e6f72c3838ebe7870c8e937cb4ea3cd
Transactions (1)
Coinbase9bd84bd53ddf76…c8e937cb4ea3cd
1 in β†’ 1 out7.2800 XPM110 B
AV6gKZLH…HRimzWbc
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.

2.586 Γ— 10⁹⁢(97-digit number)
25860133699954953014…10375829991342559359
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
2.586 Γ— 10⁹⁢(97-digit number)
25860133699954953014…10375829991342559359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.172 Γ— 10⁹⁢(97-digit number)
51720267399909906028…20751659982685118719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.034 Γ— 10⁹⁷(98-digit number)
10344053479981981205…41503319965370237439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.068 Γ— 10⁹⁷(98-digit number)
20688106959963962411…83006639930740474879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.137 Γ— 10⁹⁷(98-digit number)
41376213919927924823…66013279861480949759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.275 Γ— 10⁹⁷(98-digit number)
82752427839855849646…32026559722961899519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.655 Γ— 10⁹⁸(99-digit number)
16550485567971169929…64053119445923799039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.310 Γ— 10⁹⁸(99-digit number)
33100971135942339858…28106238891847598079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.620 Γ— 10⁹⁸(99-digit number)
66201942271884679716…56212477783695196159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.324 Γ— 10⁹⁹(100-digit number)
13240388454376935943…12424955567390392319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.648 Γ— 10⁹⁹(100-digit number)
26480776908753871886…24849911134780784639
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:57,989,889 XPMΒ·at block #6,843,189 Β· updates every 60s
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