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Block #2,344,371

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/20/2017, 4:25:08 PM Β· Difficulty 10.9011 Β· 4,489,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
607cfd482d14d7a24269f4c1e50bbb4cd1fedc4dae3e993953647bc0d759f59e
View on Chainz β†—

Height

#2,344,371

Difficulty

10.901114

Transactions

2

Size

52.02 KB

Version

2

Bits

0ae6af68

Nonce

511,824,516

Timestamp

10/20/2017, 4:25:08 PM

Confirmations

4,489,524

Mined by

⛏️ P2SHANWRaRVxQC3ktC6JgedVsHZobu4ss5EvQ9

Merkle Root

1922f930539a35a4a3f6dc62da69a0f415513fe89c1e0b74283a28dba8e99525
Transactions (2)
Coinbase664f6392758de2…8b0244bd2e249e
1 in β†’ 1 out8.9400 XPM110 B
ANWRaRVx…4ss5EvQ9
38a04714a7c0a3…c021461297388b
358 in β†’ 2 out1445.4828 XPM51.83 KB
AbUhPi9K…qLkHoNebAM9RS5dK…3EmifoPr
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.

1.271 Γ— 10⁹⁴(95-digit number)
12713666282574149066…57570545244619140501
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
1.271 Γ— 10⁹⁴(95-digit number)
12713666282574149066…57570545244619140501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.542 Γ— 10⁹⁴(95-digit number)
25427332565148298133…15141090489238281001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.085 Γ— 10⁹⁴(95-digit number)
50854665130296596267…30282180978476562001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.017 Γ— 10⁹⁡(96-digit number)
10170933026059319253…60564361956953124001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.034 Γ— 10⁹⁡(96-digit number)
20341866052118638506…21128723913906248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.068 Γ— 10⁹⁡(96-digit number)
40683732104237277013…42257447827812496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.136 Γ— 10⁹⁡(96-digit number)
81367464208474554027…84514895655624992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.627 Γ— 10⁹⁢(97-digit number)
16273492841694910805…69029791311249984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.254 Γ— 10⁹⁢(97-digit number)
32546985683389821611…38059582622499968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.509 Γ— 10⁹⁢(97-digit number)
65093971366779643222…76119165244999936001
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
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