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Block #3,503,423

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2020, 5:06:30 AM Β· Difficulty 10.9308 Β· 3,338,635 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
344d4b30010555aa993cf1b07268bd8e93eb52da87cdfee51e79965302d3a290
View on Chainz β†—

Height

#3,503,423

Difficulty

10.930826

Transactions

1

Size

199 B

Version

2

Bits

0aee4a9a

Nonce

1,089,431,173

Timestamp

1/7/2020, 5:06:30 AM

Confirmations

3,338,635

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

3fe6bdd7c93ab835f8c00bda33db59aba3b5b4731444c2ee8cf8b395c787b865
Transactions (1)
Coinbase3fe6bdd7c93ab8…f8b395c787b865
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.103 Γ— 10⁹³(94-digit number)
21033219455933385414…74070484622394426719
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
2.103 Γ— 10⁹³(94-digit number)
21033219455933385414…74070484622394426719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.206 Γ— 10⁹³(94-digit number)
42066438911866770829…48140969244788853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.413 Γ— 10⁹³(94-digit number)
84132877823733541659…96281938489577706879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁴(95-digit number)
16826575564746708331…92563876979155413759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.365 Γ— 10⁹⁴(95-digit number)
33653151129493416663…85127753958310827519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.730 Γ— 10⁹⁴(95-digit number)
67306302258986833327…70255507916621655039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.346 Γ— 10⁹⁡(96-digit number)
13461260451797366665…40511015833243310079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.692 Γ— 10⁹⁡(96-digit number)
26922520903594733330…81022031666486620159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.384 Γ— 10⁹⁡(96-digit number)
53845041807189466661…62044063332973240319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁢(97-digit number)
10769008361437893332…24088126665946480639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,980,846 XPMΒ·at block #6,842,057 Β· updates every 60s
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