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Block #213,462

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 9:28:22 PM Β· Difficulty 9.9216 Β· 6,582,431 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01ed400bfad11e489d8d16ae092b72eeda576014aa51773975c52157b7d764f5
View on Chainz β†—

Height

#213,462

Difficulty

9.921562

Transactions

1

Size

197 B

Version

2

Bits

09ebeb84

Nonce

31,912

Timestamp

10/16/2013, 9:28:22 PM

Confirmations

6,582,431

Mined by

⛏️ P2SHAK9vVy2joHqUBrbiHFhRPZZcZJniNoc5U8

Merkle Root

86ea924cf2b4d8534e87f8c89aca204ac67eca7e7661f61d5ad1709c0e8f0041
Transactions (1)
Coinbase86ea924cf2b4d8…d1709c0e8f0041
1 in β†’ 1 out10.1400 XPM109 B
AK9vVy2j…niNoc5U8
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.

8.836 Γ— 10⁹⁰(91-digit number)
88361366642925110967…00993496933156621961
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
8.836 Γ— 10⁹⁰(91-digit number)
88361366642925110967…00993496933156621961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.767 Γ— 10⁹¹(92-digit number)
17672273328585022193…01986993866313243921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.534 Γ— 10⁹¹(92-digit number)
35344546657170044386…03973987732626487841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.068 Γ— 10⁹¹(92-digit number)
70689093314340088773…07947975465252975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.413 Γ— 10⁹²(93-digit number)
14137818662868017754…15895950930505951361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.827 Γ— 10⁹²(93-digit number)
28275637325736035509…31791901861011902721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.655 Γ— 10⁹²(93-digit number)
56551274651472071018…63583803722023805441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.131 Γ— 10⁹³(94-digit number)
11310254930294414203…27167607444047610881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.262 Γ— 10⁹³(94-digit number)
22620509860588828407…54335214888095221761
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
Circulating Supply:57,611,227 XPMΒ·at block #6,795,892 Β· updates every 60s
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