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Block #2,924,325

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2018, 5:41:04 PM Β· Difficulty 11.3606 Β· 3,920,595 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7cd40241798b8f6d648c0afe01f2f9bde4cd87979deca0aae5329be50f98c05
View on Chainz β†—

Height

#2,924,325

Difficulty

11.360605

Transactions

1

Size

201 B

Version

2

Bits

0b5c509a

Nonce

1,841,178,179

Timestamp

11/15/2018, 5:41:04 PM

Confirmations

3,920,595

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

93c84253647b62993adafaed5c3598b140bb087163d3716ebd78894d9a8a1acb
Transactions (1)
Coinbase93c84253647b62…78894d9a8a1acb
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
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.

4.561 Γ— 10⁹⁷(98-digit number)
45617483605406320405…35529540717590015999
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
4.561 Γ— 10⁹⁷(98-digit number)
45617483605406320405…35529540717590015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.123 Γ— 10⁹⁷(98-digit number)
91234967210812640810…71059081435180031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.824 Γ— 10⁹⁸(99-digit number)
18246993442162528162…42118162870360063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.649 Γ— 10⁹⁸(99-digit number)
36493986884325056324…84236325740720127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.298 Γ— 10⁹⁸(99-digit number)
72987973768650112648…68472651481440255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.459 Γ— 10⁹⁹(100-digit number)
14597594753730022529…36945302962880511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.919 Γ— 10⁹⁹(100-digit number)
29195189507460045059…73890605925761023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.839 Γ— 10⁹⁹(100-digit number)
58390379014920090118…47781211851522047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.167 Γ— 10¹⁰⁰(101-digit number)
11678075802984018023…95562423703044095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.335 Γ— 10¹⁰⁰(101-digit number)
23356151605968036047…91124847406088191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.671 Γ— 10¹⁰⁰(101-digit number)
46712303211936072094…82249694812176383999
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:58,003,777 XPMΒ·at block #6,844,919 Β· updates every 60s
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