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Block #165,623

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/15/2013, 10:06:35 AM Β· Difficulty 9.8657 Β· 6,638,463 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f4e289fe243e0c4beba17c968162eb0a2a4d5a67b29b2c7158ec0daf003254b
View on Chainz β†—

Height

#165,623

Difficulty

9.865735

Transactions

2

Size

574 B

Version

2

Bits

09dda0d6

Nonce

72,648

Timestamp

9/15/2013, 10:06:35 AM

Confirmations

6,638,463

Mined by

⛏️ P2SHAc6gma4kPfGdt9d26RrmPmczn6t9gxhKzx

Merkle Root

6698dc9bcfe2391328c93d00131c902100343fd079ec8899c968ba6ee2b98634
Transactions (2)
Coinbasec73f79f3751818…0667e0643a3c4b
1 in β†’ 1 out10.2700 XPM109 B
Ac6gma4k…t9gxhKzx
68eae4fe81b12f…8589cdc5f99ba7
2 in β†’ 2 out1.1760 XPM375 B
AXxQdUca…Gd87e8PUASDPh2mv…Qm7FGzpe
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.

2.144 Γ— 10⁹⁡(96-digit number)
21447527248540504750…30134442451029649919
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
2.144 Γ— 10⁹⁡(96-digit number)
21447527248540504750…30134442451029649919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.289 Γ— 10⁹⁡(96-digit number)
42895054497081009501…60268884902059299839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.579 Γ— 10⁹⁡(96-digit number)
85790108994162019003…20537769804118599679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.715 Γ— 10⁹⁢(97-digit number)
17158021798832403800…41075539608237199359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.431 Γ— 10⁹⁢(97-digit number)
34316043597664807601…82151079216474398719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.863 Γ— 10⁹⁢(97-digit number)
68632087195329615202…64302158432948797439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.372 Γ— 10⁹⁷(98-digit number)
13726417439065923040…28604316865897594879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.745 Γ— 10⁹⁷(98-digit number)
27452834878131846081…57208633731795189759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.490 Γ— 10⁹⁷(98-digit number)
54905669756263692162…14417267463590379519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,676,737 XPMΒ·at block #6,804,085 Β· updates every 60s
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