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Block #1,417,232

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2016, 3:05:42 PM Β· Difficulty 10.7940 Β· 5,409,164 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f6c0b36f5ebe376ba34f2165035db0f39932b3d9498dfca5a5e177a828e1efb
View on Chainz β†—

Height

#1,417,232

Difficulty

10.793962

Transactions

1

Size

199 B

Version

2

Bits

0acb4113

Nonce

926,240,491

Timestamp

1/17/2016, 3:05:42 PM

Confirmations

5,409,164

Mined by

⛏️ P2SHAFpukxFaNv4xcbpMsXrR75mjZ4gTm21fA2

Merkle Root

7039205a13c524103a4c268782a90dde5d0603aedb22f07e40d8f472fd3ec505
Transactions (1)
Coinbase7039205a13c524…d8f472fd3ec505
1 in β†’ 1 out8.5700 XPM109 B
AFpukxFa…gTm21fA2
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.

5.878 Γ— 10⁹⁡(96-digit number)
58787267088671198450…03916744835135562239
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
5.878 Γ— 10⁹⁡(96-digit number)
58787267088671198450…03916744835135562239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁢(97-digit number)
11757453417734239690…07833489670271124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.351 Γ— 10⁹⁢(97-digit number)
23514906835468479380…15666979340542248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.702 Γ— 10⁹⁢(97-digit number)
47029813670936958760…31333958681084497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.405 Γ— 10⁹⁢(97-digit number)
94059627341873917521…62667917362168995839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁷(98-digit number)
18811925468374783504…25335834724337991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.762 Γ— 10⁹⁷(98-digit number)
37623850936749567008…50671669448675983359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.524 Γ— 10⁹⁷(98-digit number)
75247701873499134016…01343338897351966719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁸(99-digit number)
15049540374699826803…02686677794703933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.009 Γ— 10⁹⁸(99-digit number)
30099080749399653606…05373355589407866879
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:57,855,307 XPMΒ·at block #6,826,395 Β· updates every 60s
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