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Block #428,279

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/3/2014, 11:13:59 PM Β· Difficulty 10.3491 Β· 6,367,833 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5d04df5c54cb46015e5946bba33b2be462360ff200c5f3f4b2d6ebae51b8d2c8
View on Chainz β†—

Height

#428,279

Difficulty

10.349066

Transactions

1

Size

200 B

Version

2

Bits

0a595c5c

Nonce

246,153

Timestamp

3/3/2014, 11:13:59 PM

Confirmations

6,367,833

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

8415cf6f334ebea61c4f5bfb9cb0a9a8d8e2053ef914f7006bf42c199b27a791
Transactions (1)
Coinbase8415cf6f334ebe…f42c199b27a791
1 in β†’ 1 out9.3200 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

2.385 Γ— 10⁹⁸(99-digit number)
23857986862006780122…06378863336787372449
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
2.385 Γ— 10⁹⁸(99-digit number)
23857986862006780122…06378863336787372449
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.771 Γ— 10⁹⁸(99-digit number)
47715973724013560244…12757726673574744899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.543 Γ— 10⁹⁸(99-digit number)
95431947448027120488…25515453347149489799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁹(100-digit number)
19086389489605424097…51030906694298979599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.817 Γ— 10⁹⁹(100-digit number)
38172778979210848195…02061813388597959199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.634 Γ— 10⁹⁹(100-digit number)
76345557958421696390…04123626777195918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.526 Γ— 10¹⁰⁰(101-digit number)
15269111591684339278…08247253554391836799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.053 Γ— 10¹⁰⁰(101-digit number)
30538223183368678556…16494507108783673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.107 Γ— 10¹⁰⁰(101-digit number)
61076446366737357112…32989014217567347199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.221 Γ— 10¹⁰¹(102-digit number)
12215289273347471422…65978028435134694399
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:57,612,891 XPMΒ·at block #6,796,111 Β· updates every 60s
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