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Block #111,691

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2013, 2:20:20 PM Β· Difficulty 9.7116 Β· 6,691,365 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
310f27a844d101b749032bdccefb90fe451e906a1831dcc5fe013948917c4530
View on Chainz β†—

Height

#111,691

Difficulty

9.711634

Transactions

1

Size

200 B

Version

2

Bits

09b62da3

Nonce

115,051

Timestamp

8/11/2013, 2:20:20 PM

Confirmations

6,691,365

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

49705ae3992590a9db745cf933aa35f0086931f8c6cbb82a306fce93a46c3456
Transactions (1)
Coinbase49705ae3992590…6fce93a46c3456
1 in β†’ 1 out10.5900 XPM109 B
ATzEHZ7a…2eAGweip
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.

3.839 Γ— 10⁹⁷(98-digit number)
38399770109723765472…49738639950537693109
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
3.839 Γ— 10⁹⁷(98-digit number)
38399770109723765472…49738639950537693109
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.679 Γ— 10⁹⁷(98-digit number)
76799540219447530945…99477279901075386219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.535 Γ— 10⁹⁸(99-digit number)
15359908043889506189…98954559802150772439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.071 Γ— 10⁹⁸(99-digit number)
30719816087779012378…97909119604301544879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.143 Γ— 10⁹⁸(99-digit number)
61439632175558024756…95818239208603089759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.228 Γ— 10⁹⁹(100-digit number)
12287926435111604951…91636478417206179519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.457 Γ— 10⁹⁹(100-digit number)
24575852870223209902…83272956834412359039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.915 Γ— 10⁹⁹(100-digit number)
49151705740446419805…66545913668824718079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.830 Γ— 10⁹⁹(100-digit number)
98303411480892839610…33091827337649436159
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:57,668,475 XPMΒ·at block #6,803,055 Β· updates every 60s
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