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Block #1,161,129

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2015, 10:06:45 AM Β· Difficulty 10.9373 Β· 5,665,793 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a0434395c24644d3fc447536178bdca61f42f3c0fbdb74c06f31dfdec060a11b
View on Chainz β†—

Height

#1,161,129

Difficulty

10.937291

Transactions

2

Size

833 B

Version

2

Bits

0aeff24a

Nonce

680,779,994

Timestamp

7/19/2015, 10:06:45 AM

Confirmations

5,665,793

Mined by

⛏️ P2SHAPugvDVF43zHQz31t9bPAdjyKoKi1KxCiF

Merkle Root

8bd8bddaed685624beefeba4c7e848be17eb475377e4da71637e72ccb33021fc
Transactions (2)
Coinbase5170e83de10d73…fae9594c59f09d
1 in β†’ 1 out8.3600 XPM110 B
APugvDVF…Ki1KxCiF
2d675b5a9c41d7…b719db6fcea4b0
4 in β†’ 1 out1470.9900 XPM633 B
AHNccZy4…RwZSfQd3
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.

1.458 Γ— 10⁹⁡(96-digit number)
14580628965631535805…26723200258031790879
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
1.458 Γ— 10⁹⁡(96-digit number)
14580628965631535805…26723200258031790879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.916 Γ— 10⁹⁡(96-digit number)
29161257931263071610…53446400516063581759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.832 Γ— 10⁹⁡(96-digit number)
58322515862526143220…06892801032127163519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁢(97-digit number)
11664503172505228644…13785602064254327039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.332 Γ— 10⁹⁢(97-digit number)
23329006345010457288…27571204128508654079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.665 Γ— 10⁹⁢(97-digit number)
46658012690020914576…55142408257017308159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.331 Γ— 10⁹⁢(97-digit number)
93316025380041829153…10284816514034616319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.866 Γ— 10⁹⁷(98-digit number)
18663205076008365830…20569633028069232639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.732 Γ— 10⁹⁷(98-digit number)
37326410152016731661…41139266056138465279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.465 Γ— 10⁹⁷(98-digit number)
74652820304033463322…82278532112276930559
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:57,859,547 XPMΒ·at block #6,826,921 Β· updates every 60s
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