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Block #176,669

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/23/2013, 1:52:23 AM Β· Difficulty 9.8652 Β· 6,618,892 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7bf199c006d68124dea6678d9f4d0802e427d4286d363b52b73677c3946ae69a
View on Chainz β†—

Height

#176,669

Difficulty

9.865162

Transactions

1

Size

197 B

Version

2

Bits

09dd7b3f

Nonce

152,945

Timestamp

9/23/2013, 1:52:23 AM

Confirmations

6,618,892

Mined by

⛏️ P2SHAWsEijaAmPVVY4otUbJH1Yqtdf9WbDL6tH

Merkle Root

e38bf901ac47d80fdc17aa555b3fedd070b7ea72f9506515026f6242a8daa138
Transactions (1)
Coinbasee38bf901ac47d8…6f6242a8daa138
1 in β†’ 1 out10.2600 XPM109 B
AWsEijaA…9WbDL6tH
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.

8.183 Γ— 10⁸⁸(89-digit number)
81839167214904282369…41952670100368094499
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.183 Γ— 10⁸⁸(89-digit number)
81839167214904282369…41952670100368094499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.636 Γ— 10⁸⁹(90-digit number)
16367833442980856473…83905340200736188999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.273 Γ— 10⁸⁹(90-digit number)
32735666885961712947…67810680401472377999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.547 Γ— 10⁸⁹(90-digit number)
65471333771923425895…35621360802944755999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.309 Γ— 10⁹⁰(91-digit number)
13094266754384685179…71242721605889511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.618 Γ— 10⁹⁰(91-digit number)
26188533508769370358…42485443211779023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.237 Γ— 10⁹⁰(91-digit number)
52377067017538740716…84970886423558047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.047 Γ— 10⁹¹(92-digit number)
10475413403507748143…69941772847116095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.095 Γ— 10⁹¹(92-digit number)
20950826807015496286…39883545694232191999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,608,546 XPMΒ·at block #6,795,560 Β· updates every 60s
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