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Block #2,775,388

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2018, 12:00:03 AM Β· Difficulty 11.6641 Β· 4,067,140 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b2983420d69e80bfbe904d66898ea5f42becdbc4324a45b65153276893b0fde1
View on Chainz β†—

Height

#2,775,388

Difficulty

11.664126

Transactions

1

Size

199 B

Version

2

Bits

0baa042c

Nonce

145,716,813

Timestamp

8/2/2018, 12:00:03 AM

Confirmations

4,067,140

Mined by

⛏️ P2SHAcK54w8V5xunH6ERa2UXjw9CnVi8K7MRCL

Merkle Root

e074d8d1c15e604f7be2eedd6a146562b32aa526c025dbd7ea368f22937e1c79
Transactions (1)
Coinbasee074d8d1c15e60…368f22937e1c79
1 in β†’ 1 out7.3400 XPM109 B
AcK54w8V…i8K7MRCL
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.

1.161 Γ— 10⁹⁴(95-digit number)
11614278534749747734…25634454109706442039
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
1.161 Γ— 10⁹⁴(95-digit number)
11614278534749747734…25634454109706442039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.322 Γ— 10⁹⁴(95-digit number)
23228557069499495469…51268908219412884079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.645 Γ— 10⁹⁴(95-digit number)
46457114138998990938…02537816438825768159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.291 Γ— 10⁹⁴(95-digit number)
92914228277997981876…05075632877651536319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁡(96-digit number)
18582845655599596375…10151265755303072639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁡(96-digit number)
37165691311199192750…20302531510606145279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.433 Γ— 10⁹⁡(96-digit number)
74331382622398385501…40605063021212290559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.486 Γ— 10⁹⁢(97-digit number)
14866276524479677100…81210126042424581119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.973 Γ— 10⁹⁢(97-digit number)
29732553048959354200…62420252084849162239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.946 Γ— 10⁹⁢(97-digit number)
59465106097918708400…24840504169698324479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.189 Γ— 10⁹⁷(98-digit number)
11893021219583741680…49681008339396648959
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:57,984,646 XPMΒ·at block #6,842,527 Β· updates every 60s
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