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Block #172,778

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 12:24:02 PM Β· Difficulty 9.8613 Β· 6,637,076 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6aa9972a93c46fc09063aed3409be8a3c200ff246c388b5dff3be07854e37006
View on Chainz β†—

Height

#172,778

Difficulty

9.861268

Transactions

2

Size

538 B

Version

2

Bits

09dc7c0a

Nonce

85,260

Timestamp

9/20/2013, 12:24:02 PM

Confirmations

6,637,076

Mined by

⛏️ P2SHAcLeUnUgNB6pXR1fu3msW3S9mtm9WUmLnq

Merkle Root

b8e5f6791b7fad90cc4c2264384f487d291b942a6a5abc6da2d2b830fbbdb79d
Transactions (2)
Coinbase1fb3518f1ab6c2…8b94816393975c
1 in β†’ 1 out10.2800 XPM109 B
AcLeUnUg…m9WUmLnq
c3c7789ea3e532…9e2ccfeb3ca4e7
2 in β†’ 1 out30.7500 XPM339 B
AbEVNHvT…4XP8UPJZ
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.

2.582 Γ— 10⁹⁡(96-digit number)
25827369946932425944…11196159340957465361
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.582 Γ— 10⁹⁡(96-digit number)
25827369946932425944…11196159340957465361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.165 Γ— 10⁹⁡(96-digit number)
51654739893864851889…22392318681914930721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.033 Γ— 10⁹⁢(97-digit number)
10330947978772970377…44784637363829861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.066 Γ— 10⁹⁢(97-digit number)
20661895957545940755…89569274727659722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.132 Γ— 10⁹⁢(97-digit number)
41323791915091881511…79138549455319445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.264 Γ— 10⁹⁢(97-digit number)
82647583830183763022…58277098910638891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.652 Γ— 10⁹⁷(98-digit number)
16529516766036752604…16554197821277783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.305 Γ— 10⁹⁷(98-digit number)
33059033532073505209…33108395642555566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.611 Γ— 10⁹⁷(98-digit number)
66118067064147010418…66216791285111132161
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,722,919 XPMΒ·at block #6,809,853 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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