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Block #214,798

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/17/2013, 5:02:50 PM Β· Difficulty 9.9242 Β· 6,594,909 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dcde123fb365cfe5c9498c2d7099683d23ccedefadf412184c70868387c7f9d2
View on Chainz β†—

Height

#214,798

Difficulty

9.924177

Transactions

1

Size

197 B

Version

2

Bits

09ec96e4

Nonce

177,183

Timestamp

10/17/2013, 5:02:50 PM

Confirmations

6,594,909

Mined by

⛏️ P2SHAGPbvroz9hinzW2z7rW2tDLw79oN3HrusU

Merkle Root

0e8d179faee72b0cc449841bf52a36b04c3a31e6383764b4ab066dff4b317de1
Transactions (1)
Coinbase0e8d179faee72b…066dff4b317de1
1 in β†’ 1 out10.1400 XPM109 B
AGPbvroz…oN3HrusU
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.

7.043 Γ— 10⁸⁸(89-digit number)
70435099417858122877…10221841706662270821
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
7.043 Γ— 10⁸⁸(89-digit number)
70435099417858122877…10221841706662270821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.408 Γ— 10⁸⁹(90-digit number)
14087019883571624575…20443683413324541641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.817 Γ— 10⁸⁹(90-digit number)
28174039767143249151…40887366826649083281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.634 Γ— 10⁸⁹(90-digit number)
56348079534286498302…81774733653298166561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.126 Γ— 10⁹⁰(91-digit number)
11269615906857299660…63549467306596333121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.253 Γ— 10⁹⁰(91-digit number)
22539231813714599320…27098934613192666241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.507 Γ— 10⁹⁰(91-digit number)
45078463627429198641…54197869226385332481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.015 Γ— 10⁹⁰(91-digit number)
90156927254858397283…08395738452770664961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.803 Γ— 10⁹¹(92-digit number)
18031385450971679456…16791476905541329921
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:57,721,735 XPMΒ·at block #6,809,706 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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