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Block #118,826

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2013, 1:37:14 AM Β· Difficulty 9.7494 Β· 6,690,580 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0202c2a89c92b1e956f41af4493afadd6b2dddcb8b20e8e83d86bd4b4ec2dc75
View on Chainz β†—

Height

#118,826

Difficulty

9.749433

Transactions

1

Size

198 B

Version

2

Bits

09bfdadb

Nonce

398,200

Timestamp

8/16/2013, 1:37:14 AM

Confirmations

6,690,580

Mined by

⛏️ P2SHAT3dRckguQx6f5eEEVjWX7iYBwiggfceho

Merkle Root

9ec56edc1071e1295e89741a8c625aa14b310dcb6a52217095e69ad632c5e95f
Transactions (1)
Coinbase9ec56edc1071e1…e69ad632c5e95f
1 in β†’ 1 out10.5100 XPM109 B
AT3dRckg…iggfceho
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.

1.046 Γ— 10⁹³(94-digit number)
10467121101365451956…19493548825454631729
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
1.046 Γ— 10⁹³(94-digit number)
10467121101365451956…19493548825454631729
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.093 Γ— 10⁹³(94-digit number)
20934242202730903913…38987097650909263459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.186 Γ— 10⁹³(94-digit number)
41868484405461807827…77974195301818526919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.373 Γ— 10⁹³(94-digit number)
83736968810923615655…55948390603637053839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁴(95-digit number)
16747393762184723131…11896781207274107679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.349 Γ— 10⁹⁴(95-digit number)
33494787524369446262…23793562414548215359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.698 Γ— 10⁹⁴(95-digit number)
66989575048738892524…47587124829096430719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁡(96-digit number)
13397915009747778504…95174249658192861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.679 Γ— 10⁹⁡(96-digit number)
26795830019495557009…90348499316385722879
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:57,719,322 XPMΒ·at block #6,809,405 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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