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Block #2,177,494

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 2:32:14 PM Β· Difficulty 10.9230 Β· 4,663,077 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a850146f4b0d9da46bd5a180adbbf4b41749bcd393627ec3a0b7fadd58b12f43
View on Chainz β†—

Height

#2,177,494

Difficulty

10.923007

Transactions

1

Size

199 B

Version

2

Bits

0aec4a2a

Nonce

24,422,585

Timestamp

6/25/2017, 2:32:14 PM

Confirmations

4,663,077

Mined by

⛏️ P2SHALnQAUkpKqWLk8ZRqKm1T7Kw6132wUYhKn

Merkle Root

50a5b9898da704a28313e4eb75b9298934e018ca2de2e2d97c0eae5dd323bb11
Transactions (1)
Coinbase50a5b9898da704…0eae5dd323bb11
1 in β†’ 1 out8.3700 XPM109 B
ALnQAUkp…32wUYhKn
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.

1.502 Γ— 10⁹⁡(96-digit number)
15027002291291318142…87968838892973452799
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
1.502 Γ— 10⁹⁡(96-digit number)
15027002291291318142…87968838892973452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.005 Γ— 10⁹⁡(96-digit number)
30054004582582636284…75937677785946905599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.010 Γ— 10⁹⁡(96-digit number)
60108009165165272568…51875355571893811199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.202 Γ— 10⁹⁢(97-digit number)
12021601833033054513…03750711143787622399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.404 Γ— 10⁹⁢(97-digit number)
24043203666066109027…07501422287575244799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.808 Γ— 10⁹⁢(97-digit number)
48086407332132218054…15002844575150489599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.617 Γ— 10⁹⁢(97-digit number)
96172814664264436109…30005689150300979199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.923 Γ— 10⁹⁷(98-digit number)
19234562932852887221…60011378300601958399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.846 Γ— 10⁹⁷(98-digit number)
38469125865705774443…20022756601203916799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.693 Γ— 10⁹⁷(98-digit number)
76938251731411548887…40045513202407833599
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:57,968,903 XPMΒ·at block #6,840,570 Β· updates every 60s
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