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Block #194,091

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2013, 10:17:23 PM Β· Difficulty 9.8782 Β· 6,615,005 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1e7aaa5118520bc0c06e0897f48795d3830e0129b5457c2aa0a1c718d090527a
View on Chainz β†—

Height

#194,091

Difficulty

9.878238

Transactions

1

Size

198 B

Version

2

Bits

09e0d432

Nonce

272,852

Timestamp

10/4/2013, 10:17:23 PM

Confirmations

6,615,005

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

75cc58c81c69de15de098746f3b886f8f4dd6af13dba6a90f49ac3f6ce445f7e
Transactions (1)
Coinbase75cc58c81c69de…9ac3f6ce445f7e
1 in β†’ 1 out10.2300 XPM109 B
AKgiTbag…MJA8ujWZ
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.

3.275 Γ— 10⁹²(93-digit number)
32752802157042597840…39229990792155491479
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
3.275 Γ— 10⁹²(93-digit number)
32752802157042597840…39229990792155491479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.550 Γ— 10⁹²(93-digit number)
65505604314085195681…78459981584310982959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.310 Γ— 10⁹³(94-digit number)
13101120862817039136…56919963168621965919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.620 Γ— 10⁹³(94-digit number)
26202241725634078272…13839926337243931839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.240 Γ— 10⁹³(94-digit number)
52404483451268156545…27679852674487863679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁴(95-digit number)
10480896690253631309…55359705348975727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.096 Γ— 10⁹⁴(95-digit number)
20961793380507262618…10719410697951454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.192 Γ— 10⁹⁴(95-digit number)
41923586761014525236…21438821395902909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.384 Γ— 10⁹⁴(95-digit number)
83847173522029050472…42877642791805818879
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:57,716,830 XPMΒ·at block #6,809,095 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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