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Block #178,547

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2013, 11:37:16 AM Β· Difficulty 9.8631 Β· 6,632,536 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4a8ff44f3391b552e8ea18f426b0afff037cae185cce257c2985db6f9efe39b
View on Chainz β†—

Height

#178,547

Difficulty

9.863146

Transactions

2

Size

537 B

Version

2

Bits

09dcf71d

Nonce

99,298

Timestamp

9/24/2013, 11:37:16 AM

Confirmations

6,632,536

Mined by

⛏️ P2SHAYXUk3JzJw1h4cbgzgc56gWX2KgGU5E9Nr

Merkle Root

fbbae16a07532c888a5686aa0c683d01b8e976d013d88339d759fcb00f94fc04
Transactions (2)
Coinbase248803a48f442e…af99f66445a190
1 in β†’ 1 out10.2700 XPM109 B
AYXUk3Jz…gGU5E9Nr
2c87eb3dd0119c…274d39f9cd9498
2 in β†’ 1 out153.9900 XPM339 B
AZD5zWVk…WaHRqp5F
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.

2.142 Γ— 10⁹³(94-digit number)
21426130887031438875…59639515809384907859
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
2.142 Γ— 10⁹³(94-digit number)
21426130887031438875…59639515809384907859
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.285 Γ— 10⁹³(94-digit number)
42852261774062877750…19279031618769815719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.570 Γ— 10⁹³(94-digit number)
85704523548125755500…38558063237539631439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁴(95-digit number)
17140904709625151100…77116126475079262879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁴(95-digit number)
34281809419250302200…54232252950158525759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.856 Γ— 10⁹⁴(95-digit number)
68563618838500604400…08464505900317051519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁡(96-digit number)
13712723767700120880…16929011800634103039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁡(96-digit number)
27425447535400241760…33858023601268206079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.485 Γ— 10⁹⁡(96-digit number)
54850895070800483520…67716047202536412159
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:57,732,771 XPMΒ·at block #6,811,082 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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