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Block #169,721

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2013, 5:59:53 AM Β· Difficulty 9.8666 Β· 6,625,099 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8c428ad715630bc9d279911aa831a0d0e4f6585f3e549d557864a87ef2ef514
View on Chainz β†—

Height

#169,721

Difficulty

9.866587

Transactions

1

Size

198 B

Version

2

Bits

09ddd8a2

Nonce

70,802

Timestamp

9/18/2013, 5:59:53 AM

Confirmations

6,625,099

Mined by

⛏️ P2SHAcrXkx8MtAxrjWsXe8rTH4v6wMtKGb6K4t

Merkle Root

c4fa4190196751778a6199d9155ad0b1f088f18029b92f97d3cba03186a946b6
Transactions (1)
Coinbasec4fa4190196751…cba03186a946b6
1 in β†’ 1 out10.2600 XPM109 B
AcrXkx8M…tKGb6K4t
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.

8.139 Γ— 10⁹¹(92-digit number)
81392635505445802851…72823237225928108961
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
8.139 Γ— 10⁹¹(92-digit number)
81392635505445802851…72823237225928108961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.627 Γ— 10⁹²(93-digit number)
16278527101089160570…45646474451856217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.255 Γ— 10⁹²(93-digit number)
32557054202178321140…91292948903712435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.511 Γ— 10⁹²(93-digit number)
65114108404356642281…82585897807424871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.302 Γ— 10⁹³(94-digit number)
13022821680871328456…65171795614849743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.604 Γ— 10⁹³(94-digit number)
26045643361742656912…30343591229699486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.209 Γ— 10⁹³(94-digit number)
52091286723485313825…60687182459398973441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.041 Γ— 10⁹⁴(95-digit number)
10418257344697062765…21374364918797946881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.083 Γ— 10⁹⁴(95-digit number)
20836514689394125530…42748729837595893761
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:57,602,608 XPMΒ·at block #6,794,819 Β· updates every 60s
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