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Block #2,795,528

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/15/2018, 7:36:34 PM Β· Difficulty 11.6807 Β· 4,047,459 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7b2c21152ec15348e46e8678ad47d496f5f3ee2bcc151c28c89b2798789f098d
View on Chainz β†—

Height

#2,795,528

Difficulty

11.680717

Transactions

1

Size

201 B

Version

2

Bits

0bae4374

Nonce

109,375,232

Timestamp

8/15/2018, 7:36:34 PM

Confirmations

4,047,459

Mined by

⛏️ P2SHAdgSsdZjvuC1P88nhSnQimYDdQBMSrzQcv

Merkle Root

f9668ae5853f6dae528c1856c6922368c0e0e0df7b9be7ce2cd76f9716488344
Transactions (1)
Coinbasef9668ae5853f6d…d76f9716488344
1 in β†’ 1 out7.3200 XPM110 B
AdgSsdZj…BMSrzQcv
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.

1.382 Γ— 10⁹⁢(97-digit number)
13825672162208364168…61341964689782915839
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
1.382 Γ— 10⁹⁢(97-digit number)
13825672162208364168…61341964689782915839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁢(97-digit number)
27651344324416728336…22683929379565831679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.530 Γ— 10⁹⁢(97-digit number)
55302688648833456672…45367858759131663359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁷(98-digit number)
11060537729766691334…90735717518263326719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁷(98-digit number)
22121075459533382668…81471435036526653439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.424 Γ— 10⁹⁷(98-digit number)
44242150919066765337…62942870073053306879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.848 Γ— 10⁹⁷(98-digit number)
88484301838133530675…25885740146106613759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.769 Γ— 10⁹⁸(99-digit number)
17696860367626706135…51771480292213227519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.539 Γ— 10⁹⁸(99-digit number)
35393720735253412270…03542960584426455039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.078 Γ— 10⁹⁸(99-digit number)
70787441470506824540…07085921168852910079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁹(100-digit number)
14157488294101364908…14171842337705820159
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:57,988,251 XPMΒ·at block #6,842,986 Β· updates every 60s
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