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Block #2,120,241

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/17/2017, 6:15:21 AM Β· Difficulty 10.9117 Β· 4,723,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
06ce9b6d563d452f32cb8b1373fe443530c2e30ad138dd48c04c1bc44d095984
View on Chainz β†—

Height

#2,120,241

Difficulty

10.911688

Transactions

1

Size

242 B

Version

2

Bits

0ae96462

Nonce

293,480,222

Timestamp

5/17/2017, 6:15:21 AM

Confirmations

4,723,493

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

7b69f375ff36efcc61830b5599b11dbc7c6c1e213bc84851141435d352477696
Transactions (1)
Coinbase7b69f375ff36ef…1435d352477696
1 in β†’ 2 out8.3900 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

4.336 Γ— 10⁹⁡(96-digit number)
43366719135739917476…16068703410413072959
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
4.336 Γ— 10⁹⁡(96-digit number)
43366719135739917476…16068703410413072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.673 Γ— 10⁹⁡(96-digit number)
86733438271479834952…32137406820826145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁢(97-digit number)
17346687654295966990…64274813641652291839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.469 Γ— 10⁹⁢(97-digit number)
34693375308591933980…28549627283304583679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.938 Γ— 10⁹⁢(97-digit number)
69386750617183867961…57099254566609167359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁷(98-digit number)
13877350123436773592…14198509133218334719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁷(98-digit number)
27754700246873547184…28397018266436669439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.550 Γ— 10⁹⁷(98-digit number)
55509400493747094369…56794036532873338879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁸(99-digit number)
11101880098749418873…13588073065746677759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁸(99-digit number)
22203760197498837747…27176146131493355519
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:57,994,239 XPMΒ·at block #6,843,733 Β· updates every 60s
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