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Block #173,186

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 7:06:36 PM Β· Difficulty 9.8614 Β· 6,632,706 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c0fe3f89098409d907fe12666fa2d502280b8e22d8baa60158b96034052151fe
View on Chainz β†—

Height

#173,186

Difficulty

9.861439

Transactions

1

Size

199 B

Version

2

Bits

09dc8744

Nonce

37,689

Timestamp

9/20/2013, 7:06:36 PM

Confirmations

6,632,706

Mined by

⛏️ P2SHALefmcuDW4F9iECbUGXjGP8npv6bSfgMPT

Merkle Root

5e225c77b8ec28e62398e13b810a71ee282a82209b234abc775d820f391a9a1f
Transactions (1)
Coinbase5e225c77b8ec28…5d820f391a9a1f
1 in β†’ 1 out10.2700 XPM109 B
ALefmcuD…6bSfgMPT
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.

8.637 Γ— 10⁹³(94-digit number)
86372531768968394349…09438713421473880001
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
8.637 Γ— 10⁹³(94-digit number)
86372531768968394349…09438713421473880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.727 Γ— 10⁹⁴(95-digit number)
17274506353793678869…18877426842947760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.454 Γ— 10⁹⁴(95-digit number)
34549012707587357739…37754853685895520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.909 Γ— 10⁹⁴(95-digit number)
69098025415174715479…75509707371791040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.381 Γ— 10⁹⁡(96-digit number)
13819605083034943095…51019414743582080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.763 Γ— 10⁹⁡(96-digit number)
27639210166069886191…02038829487164160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.527 Γ— 10⁹⁡(96-digit number)
55278420332139772383…04077658974328320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.105 Γ— 10⁹⁢(97-digit number)
11055684066427954476…08155317948656640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.211 Γ— 10⁹⁢(97-digit number)
22111368132855908953…16310635897313280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.422 Γ— 10⁹⁢(97-digit number)
44222736265711817906…32621271794626560001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,691,222 XPMΒ·at block #6,805,891 Β· updates every 60s
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