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Block #113,121

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 8:52:55 AM Β· Difficulty 9.7294 Β· 6,692,726 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
236e8688e0d38c1086c3ba13bed0237adc61ac52d194c95b6657671126aabd95
View on Chainz β†—

Height

#113,121

Difficulty

9.729360

Transactions

3

Size

521 B

Version

2

Bits

09bab74f

Nonce

154,728

Timestamp

8/12/2013, 8:52:55 AM

Confirmations

6,692,726

Mined by

⛏️ P2SHAT3nVJxcWw14BGGgscnFNUtye35Ks9ypjW

Merkle Root

70a62f122d675f7f0b863434cb68c5913dea47a5d92c9c0cc0f59bd528a2bc20
Transactions (3)
Coinbasea0ff1b93a7f6fe…0e0ee77b1a0c63
1 in β†’ 1 out10.5700 XPM109 B
AT3nVJxc…5Ks9ypjW
eaac76bced3fb3…02287c9c9a730d
1 in β†’ 1 out10.7100 XPM159 B
AXkGUvU8…3ZLG8EHC
813ba94f4371ae…2b318aaeeaf8f3
1 in β†’ 1 out10.6600 XPM159 B
AQj5CF31…Sfv2KzXY
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.

3.383 Γ— 10¹⁰³(104-digit number)
33835802268524709788…68037926601539850679
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
3.383 Γ— 10¹⁰³(104-digit number)
33835802268524709788…68037926601539850679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.767 Γ— 10¹⁰³(104-digit number)
67671604537049419577…36075853203079701359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.353 Γ— 10¹⁰⁴(105-digit number)
13534320907409883915…72151706406159402719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.706 Γ— 10¹⁰⁴(105-digit number)
27068641814819767831…44303412812318805439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.413 Γ— 10¹⁰⁴(105-digit number)
54137283629639535662…88606825624637610879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.082 Γ— 10¹⁰⁡(106-digit number)
10827456725927907132…77213651249275221759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.165 Γ— 10¹⁰⁡(106-digit number)
21654913451855814264…54427302498550443519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.330 Γ— 10¹⁰⁡(106-digit number)
43309826903711628529…08854604997100887039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.661 Γ— 10¹⁰⁡(106-digit number)
86619653807423257059…17709209994201774079
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:57,690,856 XPMΒ·at block #6,805,846 Β· updates every 60s
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