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Block #221,584

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 3:53:26 PM Β· Difficulty 9.9393 Β· 6,579,789 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
621dee69e90fe8cd35fa2c85fbc3bd3fef7b1becad4f4b95653da839d66fd368
View on Chainz β†—

Height

#221,584

Difficulty

9.939297

Transactions

1

Size

204 B

Version

2

Bits

09f075c4

Nonce

16,777,375

Timestamp

10/21/2013, 3:53:26 PM

Confirmations

6,579,789

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

c358cdf65b65ae354fc1190ca8785146d2e3eb7851b62f4b7ce12857a47c519b
Transactions (1)
Coinbasec358cdf65b65ae…e12857a47c519b
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.535 Γ— 10⁹⁰(91-digit number)
45354799686314733295…76064879616827607821
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
4.535 Γ— 10⁹⁰(91-digit number)
45354799686314733295…76064879616827607821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.070 Γ— 10⁹⁰(91-digit number)
90709599372629466591…52129759233655215641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.814 Γ— 10⁹¹(92-digit number)
18141919874525893318…04259518467310431281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.628 Γ— 10⁹¹(92-digit number)
36283839749051786636…08519036934620862561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.256 Γ— 10⁹¹(92-digit number)
72567679498103573273…17038073869241725121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.451 Γ— 10⁹²(93-digit number)
14513535899620714654…34076147738483450241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.902 Γ— 10⁹²(93-digit number)
29027071799241429309…68152295476966900481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.805 Γ— 10⁹²(93-digit number)
58054143598482858618…36304590953933800961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.161 Γ— 10⁹³(94-digit number)
11610828719696571723…72609181907867601921
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:57,655,057 XPMΒ·at block #6,801,372 Β· updates every 60s
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