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Block #172,818

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 1:11:42 PM Β· Difficulty 9.8611 Β· 6,636,514 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
593882e6c7a452ede3978c86ce423647263889ffc6b549f99b02377115da125d
View on Chainz β†—

Height

#172,818

Difficulty

9.861127

Transactions

1

Size

198 B

Version

2

Bits

09dc72cb

Nonce

414,386

Timestamp

9/20/2013, 1:11:42 PM

Confirmations

6,636,514

Mined by

⛏️ P2SHAcLeUnUgNB6pXR1fu3msW3S9mtm9WUmLnq

Merkle Root

146e2ab1c669ece7aad9fe7c215d151cdeecc228b674aef4f40334a43e0265d6
Transactions (1)
Coinbase146e2ab1c669ec…0334a43e0265d6
1 in β†’ 1 out10.2700 XPM109 B
AcLeUnUg…m9WUmLnq
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.

1.321 Γ— 10⁹³(94-digit number)
13219079930169889261…60856382048822865941
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
1.321 Γ— 10⁹³(94-digit number)
13219079930169889261…60856382048822865941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.643 Γ— 10⁹³(94-digit number)
26438159860339778523…21712764097645731881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.287 Γ— 10⁹³(94-digit number)
52876319720679557047…43425528195291463761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.057 Γ— 10⁹⁴(95-digit number)
10575263944135911409…86851056390582927521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.115 Γ— 10⁹⁴(95-digit number)
21150527888271822818…73702112781165855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.230 Γ— 10⁹⁴(95-digit number)
42301055776543645637…47404225562331710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.460 Γ— 10⁹⁴(95-digit number)
84602111553087291275…94808451124663420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.692 Γ— 10⁹⁡(96-digit number)
16920422310617458255…89616902249326840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.384 Γ— 10⁹⁡(96-digit number)
33840844621234916510…79233804498653680641
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:57,718,722 XPMΒ·at block #6,809,331 Β· updates every 60s
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