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Block #452,422

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/20/2014, 1:55:10 PM Β· Difficulty 10.3912 Β· 6,342,035 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
03625d0f0a67c4225881319646dbb49b02b2ca3078dd0d33eb337d46edfa3906
View on Chainz β†—

Height

#452,422

Difficulty

10.391187

Transactions

2

Size

580 B

Version

2

Bits

0a6424d1

Nonce

51,484,378

Timestamp

3/20/2014, 1:55:10 PM

Confirmations

6,342,035

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1e8844769e0b09b7ad0d28e1fa8d56ea316af9924b00c2db77aedb1a9fba1b6c
Transactions (2)
Coinbase50a6934023c8f9…d8a26e74d44065
1 in β†’ 1 out9.2600 XPM116 B
AbwWkWZt…kawDhufa
037c751a81d4c8…5df467519af607
2 in β†’ 2 out138.9100 XPM374 B
AQUC7Hue…LL2XMoNYAcVP535h…4K9VBKjp
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.

1.215 Γ— 10⁹⁴(95-digit number)
12158555671718450638…00412215013273472999
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
1.215 Γ— 10⁹⁴(95-digit number)
12158555671718450638…00412215013273472999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.431 Γ— 10⁹⁴(95-digit number)
24317111343436901276…00824430026546945999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.863 Γ— 10⁹⁴(95-digit number)
48634222686873802552…01648860053093891999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.726 Γ— 10⁹⁴(95-digit number)
97268445373747605104…03297720106187783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.945 Γ— 10⁹⁡(96-digit number)
19453689074749521020…06595440212375567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.890 Γ— 10⁹⁡(96-digit number)
38907378149499042041…13190880424751135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.781 Γ— 10⁹⁡(96-digit number)
77814756298998084083…26381760849502271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.556 Γ— 10⁹⁢(97-digit number)
15562951259799616816…52763521699004543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.112 Γ— 10⁹⁢(97-digit number)
31125902519599233633…05527043398009087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.225 Γ— 10⁹⁢(97-digit number)
62251805039198467267…11054086796018175999
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:57,599,697 XPMΒ·at block #6,794,456 Β· updates every 60s
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