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Block #10,326

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 2:36:12 AM Β· Difficulty 7.6660 Β· 6,816,388 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2863ddb421a88ec2a5a64bd1088356acd3ea6653bff9fbb4dd0a3530c45a9579
View on Chainz β†—

Height

#10,326

Difficulty

7.665977

Transactions

1

Size

197 B

Version

2

Bits

07aa7d7f

Nonce

274

Timestamp

7/11/2013, 2:36:12 AM

Confirmations

6,816,388

Mined by

⛏️ P2SHATdcg5aGsKSGVEp9Y9eFvZwDgeu44DE6Kp

Merkle Root

e6b808bc317e84fbb8da213dd87624a845608eafa8d098397b7df955e4a24a03
Transactions (1)
Coinbasee6b808bc317e84…7df955e4a24a03
1 in β†’ 1 out16.9900 XPM109 B
ATdcg5aG…u44DE6Kp
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.

1.004 Γ— 10⁸⁹(90-digit number)
10042682855486812656…67819843270677316599
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
1.004 Γ— 10⁸⁹(90-digit number)
10042682855486812656…67819843270677316599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.008 Γ— 10⁸⁹(90-digit number)
20085365710973625312…35639686541354633199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.017 Γ— 10⁸⁹(90-digit number)
40170731421947250624…71279373082709266399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.034 Γ— 10⁸⁹(90-digit number)
80341462843894501249…42558746165418532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.606 Γ— 10⁹⁰(91-digit number)
16068292568778900249…85117492330837065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.213 Γ— 10⁹⁰(91-digit number)
32136585137557800499…70234984661674131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.427 Γ— 10⁹⁰(91-digit number)
64273170275115600999…40469969323348262399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,857,865 XPMΒ·at block #6,826,713 Β· updates every 60s
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