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Block #212,518

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 8:27:42 AM Β· Difficulty 9.9189 Β· 6,632,191 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a589a513f5a5541b6e9451e05bb1f4da7eeb6d839ec24d56affe35dfc296518a
View on Chainz β†—

Height

#212,518

Difficulty

9.918947

Transactions

1

Size

201 B

Version

2

Bits

09eb401e

Nonce

21,393

Timestamp

10/16/2013, 8:27:42 AM

Confirmations

6,632,191

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

ef31edc6bbf702aae42a1610e9e95242350c68c9c5373017c7ad2bbfaf08cea2
Transactions (1)
Coinbaseef31edc6bbf702…ad2bbfaf08cea2
1 in β†’ 1 out10.1500 XPM110 B
AbuU1HhS…JPwsJEbB
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.

4.444 Γ— 10⁹⁢(97-digit number)
44442261823592789775…09856984642420424001
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
4.444 Γ— 10⁹⁢(97-digit number)
44442261823592789775…09856984642420424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.888 Γ— 10⁹⁢(97-digit number)
88884523647185579551…19713969284840848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.777 Γ— 10⁹⁷(98-digit number)
17776904729437115910…39427938569681696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.555 Γ— 10⁹⁷(98-digit number)
35553809458874231820…78855877139363392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.110 Γ— 10⁹⁷(98-digit number)
71107618917748463641…57711754278726784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.422 Γ— 10⁹⁸(99-digit number)
14221523783549692728…15423508557453568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.844 Γ— 10⁹⁸(99-digit number)
28443047567099385456…30847017114907136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.688 Γ— 10⁹⁸(99-digit number)
56886095134198770913…61694034229814272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.137 Γ— 10⁹⁹(100-digit number)
11377219026839754182…23388068459628544001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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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