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Block #173,483

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2013, 12:49:29 AM Β· Difficulty 9.8602 Β· 6,634,092 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
20a1f141a8ab9d317cc55ce98329fb5dfcd418fdf95a295d633ca8312f0f3411
View on Chainz β†—

Height

#173,483

Difficulty

9.860182

Transactions

1

Size

199 B

Version

2

Bits

09dc34e3

Nonce

23,344

Timestamp

9/21/2013, 12:49:29 AM

Confirmations

6,634,092

Mined by

⛏️ P2SHAcLeUnUgNB6pXR1fu3msW3S9mtm9WUmLnq

Merkle Root

552a80cbfee23865c26935d0509b5d19c301445f325e93b0eb81f4ccf3def865
Transactions (1)
Coinbase552a80cbfee238…81f4ccf3def865
1 in β†’ 1 out10.2700 XPM109 B
AcLeUnUg…m9WUmLnq
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.

1.902 Γ— 10⁹⁴(95-digit number)
19027578308747439753…10766593273277892959
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
1.902 Γ— 10⁹⁴(95-digit number)
19027578308747439753…10766593273277892959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.805 Γ— 10⁹⁴(95-digit number)
38055156617494879507…21533186546555785919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.611 Γ— 10⁹⁴(95-digit number)
76110313234989759015…43066373093111571839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁡(96-digit number)
15222062646997951803…86132746186223143679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.044 Γ— 10⁹⁡(96-digit number)
30444125293995903606…72265492372446287359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.088 Γ— 10⁹⁡(96-digit number)
60888250587991807212…44530984744892574719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁢(97-digit number)
12177650117598361442…89061969489785149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.435 Γ— 10⁹⁢(97-digit number)
24355300235196722884…78123938979570298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.871 Γ— 10⁹⁢(97-digit number)
48710600470393445769…56247877959140597759
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:57,704,629 XPMΒ·at block #6,807,574 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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