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Block #163,181

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2013, 8:12:27 PM Β· Difficulty 9.8612 Β· 6,631,803 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dedf82cf06afb22e422b3282b40b5f894033f689dea06adbc625ca06885e3408
View on Chainz β†—

Height

#163,181

Difficulty

9.861175

Transactions

1

Size

199 B

Version

2

Bits

09dc75f3

Nonce

734,041

Timestamp

9/13/2013, 8:12:27 PM

Confirmations

6,631,803

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

c6e686c81b8faa747af30604381d86d5b99e51d03fba8aabeb2b8e6a635eb560
Transactions (1)
Coinbasec6e686c81b8faa…2b8e6a635eb560
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

5.249 Γ— 10⁹⁴(95-digit number)
52499287746846464721…47094850535297123439
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
5.249 Γ— 10⁹⁴(95-digit number)
52499287746846464721…47094850535297123439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁡(96-digit number)
10499857549369292944…94189701070594246879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.099 Γ— 10⁹⁡(96-digit number)
20999715098738585888…88379402141188493759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.199 Γ— 10⁹⁡(96-digit number)
41999430197477171777…76758804282376987519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.399 Γ— 10⁹⁡(96-digit number)
83998860394954343554…53517608564753975039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁢(97-digit number)
16799772078990868710…07035217129507950079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.359 Γ— 10⁹⁢(97-digit number)
33599544157981737421…14070434259015900159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.719 Γ— 10⁹⁢(97-digit number)
67199088315963474843…28140868518031800319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁷(98-digit number)
13439817663192694968…56281737036063600639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.687 Γ— 10⁹⁷(98-digit number)
26879635326385389937…12563474072127201279
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:57,603,913 XPMΒ·at block #6,794,983 Β· updates every 60s
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