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Block #2,456,465

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2018, 12:22:24 AM Β· Difficulty 10.9536 Β· 4,388,698 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2137a318ae4f1e073683c1a101740ea00937af0c87c32703ecd8dbda3a5633ec
View on Chainz β†—

Height

#2,456,465

Difficulty

10.953558

Transactions

2

Size

2.84 KB

Version

2

Bits

0af41c64

Nonce

804,042,128

Timestamp

1/4/2018, 12:22:24 AM

Confirmations

4,388,698

Mined by

⛏️ P2SHAJyLW839Z3pvWThLwhtcqi7YvcXWJGwCeN

Merkle Root

3338c98872ca12d00ce307995f514b55aa38d97fb11287dd2c9224eede10d04b
Transactions (2)
Coinbasede252a2ad7a469…a7798382d343ea
1 in β†’ 1 out8.3500 XPM109 B
AJyLW839…XWJGwCeN
6c382d2c18c7f7…babc8e802a017d
18 in β†’ 1 out68.9700 XPM2.64 KB
AH9qZNSH…7a5DCX4F
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.

1.116 Γ— 10⁹⁡(96-digit number)
11164662388200714740…06921174441865038079
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
1.116 Γ— 10⁹⁡(96-digit number)
11164662388200714740…06921174441865038079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.232 Γ— 10⁹⁡(96-digit number)
22329324776401429481…13842348883730076159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.465 Γ— 10⁹⁡(96-digit number)
44658649552802858962…27684697767460152319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.931 Γ— 10⁹⁡(96-digit number)
89317299105605717924…55369395534920304639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁢(97-digit number)
17863459821121143584…10738791069840609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.572 Γ— 10⁹⁢(97-digit number)
35726919642242287169…21477582139681218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.145 Γ— 10⁹⁢(97-digit number)
71453839284484574339…42955164279362437119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.429 Γ— 10⁹⁷(98-digit number)
14290767856896914867…85910328558724874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.858 Γ— 10⁹⁷(98-digit number)
28581535713793829735…71820657117449748479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.716 Γ— 10⁹⁷(98-digit number)
57163071427587659471…43641314234899496959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁸(99-digit number)
11432614285517531894…87282628469798993919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,005,733 XPMΒ·at block #6,845,162 Β· updates every 60s
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