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Block #2,833,288

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 3:41:00 PM Β· Difficulty 11.7152 Β· 4,005,721 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e16e0e22020f40ad455a1d658dffb8dfc2554cbec4017b9678254be4611f4c8
View on Chainz β†—

Height

#2,833,288

Difficulty

11.715185

Transactions

1

Size

200 B

Version

2

Bits

0bb71664

Nonce

1,069,442,954

Timestamp

9/10/2018, 3:41:00 PM

Confirmations

4,005,721

Mined by

⛏️ P2SHAMCpDFwb37o6y4zKKDywwPSqttJjvxXHpG

Merkle Root

89c83044d3031788a17df4a4f23f56836f9800b2c655c0eab863ea75ea7c39d5
Transactions (1)
Coinbase89c83044d30317…63ea75ea7c39d5
1 in β†’ 1 out7.2700 XPM110 B
AMCpDFwb…JjvxXHpG
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.

2.508 Γ— 10⁹⁴(95-digit number)
25085128912283998930…62906527215216940259
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
2.508 Γ— 10⁹⁴(95-digit number)
25085128912283998930…62906527215216940259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.017 Γ— 10⁹⁴(95-digit number)
50170257824567997861…25813054430433880519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁡(96-digit number)
10034051564913599572…51626108860867761039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.006 Γ— 10⁹⁡(96-digit number)
20068103129827199144…03252217721735522079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.013 Γ— 10⁹⁡(96-digit number)
40136206259654398289…06504435443471044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.027 Γ— 10⁹⁡(96-digit number)
80272412519308796578…13008870886942088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁢(97-digit number)
16054482503861759315…26017741773884176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.210 Γ— 10⁹⁢(97-digit number)
32108965007723518631…52035483547768353279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.421 Γ— 10⁹⁢(97-digit number)
64217930015447037262…04070967095536706559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.284 Γ— 10⁹⁷(98-digit number)
12843586003089407452…08141934191073413119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.568 Γ— 10⁹⁷(98-digit number)
25687172006178814905…16283868382146826239
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:57,956,338 XPMΒ·at block #6,839,008 Β· updates every 60s
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