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Block #69,352

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 8:21:09 AM Β· Difficulty 8.9908 Β· 6,733,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5eb21bea9fa818a4b4e4c3702af61092f25aa9b564fb1ee1661c9d790e8f3ff0
View on Chainz β†—

Height

#69,352

Difficulty

8.990819

Transactions

1

Size

201 B

Version

2

Bits

08fda64f

Nonce

467

Timestamp

7/20/2013, 8:21:09 AM

Confirmations

6,733,103

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

2a02463d97c4eccc7de267f6152455878c39dd208613b6e78e2fdedad9733ce9
Transactions (1)
Coinbase2a02463d97c4ec…2fdedad9733ce9
1 in β†’ 1 out12.3500 XPM109 B
AXSFye4r…ADf1YWCU
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.

2.948 Γ— 10⁹⁸(99-digit number)
29483745822858233168…24751536409813916799
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
2.948 Γ— 10⁹⁸(99-digit number)
29483745822858233168…24751536409813916799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.896 Γ— 10⁹⁸(99-digit number)
58967491645716466337…49503072819627833599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.179 Γ— 10⁹⁹(100-digit number)
11793498329143293267…99006145639255667199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.358 Γ— 10⁹⁹(100-digit number)
23586996658286586535…98012291278511334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.717 Γ— 10⁹⁹(100-digit number)
47173993316573173070…96024582557022668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.434 Γ— 10⁹⁹(100-digit number)
94347986633146346140…92049165114045337599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.886 Γ— 10¹⁰⁰(101-digit number)
18869597326629269228…84098330228090675199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.773 Γ— 10¹⁰⁰(101-digit number)
37739194653258538456…68196660456181350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.547 Γ— 10¹⁰⁰(101-digit number)
75478389306517076912…36393320912362700799
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:57,663,653 XPMΒ·at block #6,802,454 Β· updates every 60s
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