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Block #172,645

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 9:54:35 AM Β· Difficulty 9.8617 Β· 6,631,549 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52431e54df085b882b834648270d0c44f8f065c7566347271aac322de7420d29
View on Chainz β†—

Height

#172,645

Difficulty

9.861736

Transactions

2

Size

732 B

Version

2

Bits

09dc9ab8

Nonce

92,827

Timestamp

9/20/2013, 9:54:35 AM

Confirmations

6,631,549

Mined by

⛏️ P2SHAGLpT5zBCy42ej8dmuMEVvxHoCBnHeFXQg

Merkle Root

568315d964cd49cf997e67069e0b5dfb972549b82c02244c8ab0eb035cd8591d
Transactions (2)
Coinbasea83736417b1de3…83c79d7f5aa245
1 in β†’ 1 out10.2800 XPM109 B
AGLpT5zB…BnHeFXQg
21802d8c9b5248…50f3d0aa050ddc
4 in β†’ 2 out41.0500 XPM533 B
AeaQWN3n…P3dPWYUrARyYtqtL…uCP66s1P
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.

1.001 Γ— 10⁹⁴(95-digit number)
10014802549359638212…31730854439646551041
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
1.001 Γ— 10⁹⁴(95-digit number)
10014802549359638212…31730854439646551041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.002 Γ— 10⁹⁴(95-digit number)
20029605098719276425…63461708879293102081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.005 Γ— 10⁹⁴(95-digit number)
40059210197438552850…26923417758586204161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.011 Γ— 10⁹⁴(95-digit number)
80118420394877105701…53846835517172408321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.602 Γ— 10⁹⁡(96-digit number)
16023684078975421140…07693671034344816641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.204 Γ— 10⁹⁡(96-digit number)
32047368157950842280…15387342068689633281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.409 Γ— 10⁹⁡(96-digit number)
64094736315901684561…30774684137379266561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.281 Γ— 10⁹⁢(97-digit number)
12818947263180336912…61549368274758533121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.563 Γ— 10⁹⁢(97-digit number)
25637894526360673824…23098736549517066241
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:57,677,606 XPMΒ·at block #6,804,193 Β· updates every 60s
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