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Block #113,324

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 11:38:25 AM Β· Difficulty 9.7313 Β· 6,713,223 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d46ab32903196c89a40c727440ec0cde23a679d898d498c3b439ff6a8a90b12a
View on Chainz β†—

Height

#113,324

Difficulty

9.731298

Transactions

1

Size

201 B

Version

2

Bits

09bb3660

Nonce

158,987

Timestamp

8/12/2013, 11:38:25 AM

Confirmations

6,713,223

Mined by

⛏️ P2SHAMYUL1XY1HPqSCSMa5ah7SRkgVt3WZL89n

Merkle Root

3d3b4103ca86179cae22a024ce2998c8eb493e4f09a96165e1c9b541211c3643
Transactions (1)
Coinbase3d3b4103ca8617…c9b541211c3643
1 in β†’ 1 out10.5400 XPM109 B
AMYUL1XY…t3WZL89n
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.

5.232 Γ— 10⁹⁹(100-digit number)
52323397129062217635…76679545926602645889
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
5.232 Γ— 10⁹⁹(100-digit number)
52323397129062217635…76679545926602645889
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.046 Γ— 10¹⁰⁰(101-digit number)
10464679425812443527…53359091853205291779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.092 Γ— 10¹⁰⁰(101-digit number)
20929358851624887054…06718183706410583559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.185 Γ— 10¹⁰⁰(101-digit number)
41858717703249774108…13436367412821167119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.371 Γ— 10¹⁰⁰(101-digit number)
83717435406499548217…26872734825642334239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.674 Γ— 10¹⁰¹(102-digit number)
16743487081299909643…53745469651284668479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.348 Γ— 10¹⁰¹(102-digit number)
33486974162599819286…07490939302569336959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.697 Γ— 10¹⁰¹(102-digit number)
66973948325199638573…14981878605138673919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.339 Γ— 10¹⁰²(103-digit number)
13394789665039927714…29963757210277347839
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
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