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Block #2,833,146

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 1:20:47 PM Β· Difficulty 11.7151 Β· 4,010,069 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
634178a747f77aaff09b2c472b890ca312a9cef8970bd159d174bab8bec0fae4
View on Chainz β†—

Height

#2,833,146

Difficulty

11.715063

Transactions

1

Size

201 B

Version

2

Bits

0bb70e60

Nonce

1,451,286,062

Timestamp

9/10/2018, 1:20:47 PM

Confirmations

4,010,069

Mined by

⛏️ P2SHAeb9oDJ8DPVv8BtS3izJgEx4XMWjb1Swc9

Merkle Root

07e5fa286fd8b793e4146fd9bd3bcb50251fb8f7cdbdf5322dad1304aa9b04fb
Transactions (1)
Coinbase07e5fa286fd8b7…ad1304aa9b04fb
1 in β†’ 1 out7.2700 XPM110 B
Aeb9oDJ8…Wjb1Swc9
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.

1.088 Γ— 10⁹⁢(97-digit number)
10881189585607620088…98079364686071999999
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
1.088 Γ— 10⁹⁢(97-digit number)
10881189585607620088…98079364686071999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.176 Γ— 10⁹⁢(97-digit number)
21762379171215240177…96158729372143999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.352 Γ— 10⁹⁢(97-digit number)
43524758342430480355…92317458744287999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.704 Γ— 10⁹⁢(97-digit number)
87049516684860960711…84634917488575999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.740 Γ— 10⁹⁷(98-digit number)
17409903336972192142…69269834977151999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.481 Γ— 10⁹⁷(98-digit number)
34819806673944384284…38539669954303999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.963 Γ— 10⁹⁷(98-digit number)
69639613347888768569…77079339908607999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁸(99-digit number)
13927922669577753713…54158679817215999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.785 Γ— 10⁹⁸(99-digit number)
27855845339155507427…08317359634431999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.571 Γ— 10⁹⁸(99-digit number)
55711690678311014855…16634719268863999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁹(100-digit number)
11142338135662202971…33269438537727999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁹(100-digit number)
22284676271324405942…66538877075455999999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,990,093 XPMΒ·at block #6,843,214 Β· updates every 60s
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