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Block #99,345

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2013, 3:50:51 PM Β· Difficulty 9.3827 Β· 6,697,467 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
52d95504f55e4f9a5a1eb3c858754529d1c36164878ded7bbfac99db016229bb
View on Chainz β†—

Height

#99,345

Difficulty

9.382747

Transactions

2

Size

542 B

Version

2

Bits

0961fbb4

Nonce

199,732

Timestamp

8/5/2013, 3:50:51 PM

Confirmations

6,697,467

Mined by

⛏️ P2SHAYuAnvsNYsghnKHMNLtwiEHLjP7N9qViJE

Merkle Root

96ab9e8901f746415d207ece43f9dd9b5c4bda0ce182973a079df004e9cbfac5
Transactions (2)
Coinbasef6ebd23b7a649d…1be3a62bbd919a
1 in β†’ 1 out11.3500 XPM109 B
AYuAnvsN…7N9qViJE
17007436b95249…515ede8e89db17
2 in β†’ 1 out259.9900 XPM342 B
AcU3G17t…7wPGLC6Z
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.

1.079 Γ— 10⁹⁸(99-digit number)
10798894698914026488…57762759429857046189
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
1.079 Γ— 10⁹⁸(99-digit number)
10798894698914026488…57762759429857046189
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁸(99-digit number)
21597789397828052977…15525518859714092379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁸(99-digit number)
43195578795656105954…31051037719428184759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁸(99-digit number)
86391157591312211908…62102075438856369519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁹(100-digit number)
17278231518262442381…24204150877712739039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.455 Γ— 10⁹⁹(100-digit number)
34556463036524884763…48408301755425478079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.911 Γ— 10⁹⁹(100-digit number)
69112926073049769526…96816603510850956159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.382 Γ— 10¹⁰⁰(101-digit number)
13822585214609953905…93633207021701912319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.764 Γ— 10¹⁰⁰(101-digit number)
27645170429219907810…87266414043403824639
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:57,618,511 XPMΒ·at block #6,796,811 Β· updates every 60s
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