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Block #113,186

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 9:39:44 AM Β· Difficulty 9.7303 Β· 6,689,367 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a3e659a801a841b215d171380e01bbf54ed75a0c27ea65fc4639028fabd62d0a
View on Chainz β†—

Height

#113,186

Difficulty

9.730297

Transactions

2

Size

357 B

Version

2

Bits

09baf4c5

Nonce

117,987

Timestamp

8/12/2013, 9:39:44 AM

Confirmations

6,689,367

Mined by

⛏️ P2SHAbp2xWaqRTsAoqArWV9dTgcN63YFBxbAqe

Merkle Root

2340ea83f8537c5c238e2c05cfb3a04e2af2acff5e038217362f222522399294
Transactions (2)
Coinbase9a5d122d52696e…f5f9c93ea9827e
1 in β†’ 1 out10.5600 XPM109 B
Abp2xWaq…YFBxbAqe
7ad581e4ab6117…c6f71cc562f7f3
1 in β†’ 1 out10.6700 XPM157 B
AXkGUvU8…3ZLG8EHC
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.

1.474 Γ— 10⁹⁸(99-digit number)
14745378247064859687…15104331057203613259
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
1.474 Γ— 10⁹⁸(99-digit number)
14745378247064859687…15104331057203613259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.949 Γ— 10⁹⁸(99-digit number)
29490756494129719375…30208662114407226519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.898 Γ— 10⁹⁸(99-digit number)
58981512988259438751…60417324228814453039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.179 Γ— 10⁹⁹(100-digit number)
11796302597651887750…20834648457628906079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.359 Γ— 10⁹⁹(100-digit number)
23592605195303775500…41669296915257812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.718 Γ— 10⁹⁹(100-digit number)
47185210390607551000…83338593830515624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.437 Γ— 10⁹⁹(100-digit number)
94370420781215102001…66677187661031248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.887 Γ— 10¹⁰⁰(101-digit number)
18874084156243020400…33354375322062497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.774 Γ— 10¹⁰⁰(101-digit number)
37748168312486040800…66708750644124994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.549 Γ— 10¹⁰⁰(101-digit number)
75496336624972081601…33417501288249989119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,664,437 XPMΒ·at block #6,802,552 Β· updates every 60s
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