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Block #2,302,019

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2017, 3:12:05 AM Β· Difficulty 10.9274 Β· 4,542,754 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ea49bb8f7e3159299130e1887c1be2855dcd7ef125c044b5a9f54c25de75f56
View on Chainz β†—

Height

#2,302,019

Difficulty

10.927429

Transactions

1

Size

199 B

Version

2

Bits

0aed6c00

Nonce

1,654,899,840

Timestamp

9/20/2017, 3:12:05 AM

Confirmations

4,542,754

Mined by

⛏️ P2SHAZgWdNLKKgYZBZ496tMBxTy8xvDLPpUfU2

Merkle Root

c5f0b84555c5ba878392b03fee0f2f8c667a214c1c95803d1f5710574d1a6f0d
Transactions (1)
Coinbasec5f0b84555c5ba…5710574d1a6f0d
1 in β†’ 1 out8.3600 XPM109 B
AZgWdNLK…DLPpUfU2
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.

1.214 Γ— 10⁹⁴(95-digit number)
12143269345978872450…12224922751946752981
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.214 Γ— 10⁹⁴(95-digit number)
12143269345978872450…12224922751946752981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.428 Γ— 10⁹⁴(95-digit number)
24286538691957744900…24449845503893505961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.857 Γ— 10⁹⁴(95-digit number)
48573077383915489800…48899691007787011921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.714 Γ— 10⁹⁴(95-digit number)
97146154767830979600…97799382015574023841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.942 Γ— 10⁹⁡(96-digit number)
19429230953566195920…95598764031148047681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.885 Γ— 10⁹⁡(96-digit number)
38858461907132391840…91197528062296095361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.771 Γ— 10⁹⁡(96-digit number)
77716923814264783680…82395056124592190721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.554 Γ— 10⁹⁢(97-digit number)
15543384762852956736…64790112249184381441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.108 Γ— 10⁹⁢(97-digit number)
31086769525705913472…29580224498368762881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.217 Γ— 10⁹⁢(97-digit number)
62173539051411826944…59160448996737525761
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:58,002,597 XPMΒ·at block #6,844,772 Β· updates every 60s
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