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Block #165,541

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/15/2013, 8:53:55 AM Β· Difficulty 9.8655 Β· 6,636,847 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3cd5748dffa0826e17ababf0d5abed70f26d9f8a0be548e232f6f6877c95ad19
View on Chainz β†—

Height

#165,541

Difficulty

9.865501

Transactions

2

Size

698 B

Version

2

Bits

09dd917b

Nonce

41,620

Timestamp

9/15/2013, 8:53:55 AM

Confirmations

6,636,847

Mined by

⛏️ P2SHAXcstvw2xBpcWFFDpisP5FcZGKTmnmzdbL

Merkle Root

2947f9d48732e93d1134137ccc4918e0eba94502c52f98ff4378dd3302162901
Transactions (2)
Coinbasee3054c381e717d…8a623ed1d2a118
1 in β†’ 1 out10.2700 XPM109 B
AXcstvw2…TmnmzdbL
14e0f6a8f6bfd9…a1c8302a0efbbf
4 in β†’ 1 out41.1000 XPM499 B
Abg9b4kX…im9CLs7g
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.

9.677 Γ— 10⁹⁴(95-digit number)
96775875106204979121…67723118314010433599
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
9.677 Γ— 10⁹⁴(95-digit number)
96775875106204979121…67723118314010433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁡(96-digit number)
19355175021240995824…35446236628020867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.871 Γ— 10⁹⁡(96-digit number)
38710350042481991648…70892473256041734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.742 Γ— 10⁹⁡(96-digit number)
77420700084963983296…41784946512083468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.548 Γ— 10⁹⁢(97-digit number)
15484140016992796659…83569893024166937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.096 Γ— 10⁹⁢(97-digit number)
30968280033985593318…67139786048333875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.193 Γ— 10⁹⁢(97-digit number)
61936560067971186637…34279572096667750399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁷(98-digit number)
12387312013594237327…68559144193335500799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.477 Γ— 10⁹⁷(98-digit number)
24774624027188474655…37118288386671001599
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:57,663,118 XPMΒ·at block #6,802,387 Β· updates every 60s
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