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Block #170,826

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 1:29:21 AM Β· Difficulty 9.8650 Β· 6,632,621 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9c4499bf7dc4176e7dd11490fe509e0a2bd3f5c0a6a05a7c04a441343b1ccae
View on Chainz β†—

Height

#170,826

Difficulty

9.865013

Transactions

2

Size

424 B

Version

2

Bits

09dd7183

Nonce

228,282

Timestamp

9/19/2013, 1:29:21 AM

Confirmations

6,632,621

Mined by

⛏️ P2SHAKyKBBF5ebK5pPoKW1JHjRVY1fQ9vxBLNg

Merkle Root

d60fd3fa96deb88097e4856921d6154e3f24b5f5ee7d9009367a298a2fc0214a
Transactions (2)
Coinbasec505084022b6d1…cd2b628ea4453f
1 in β†’ 1 out10.2700 XPM109 B
AKyKBBF5…Q9vxBLNg
632a8ca5742a1f…ddf206ca6994b9
1 in β†’ 2 out10.2400 XPM226 B
AeU9Jshq…ogs4PQYwAaY836zh…CsLxD4Yg
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.

9.407 Γ— 10⁹²(93-digit number)
94070603934522471350…41447380814948431681
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
9.407 Γ— 10⁹²(93-digit number)
94070603934522471350…41447380814948431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.881 Γ— 10⁹³(94-digit number)
18814120786904494270…82894761629896863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.762 Γ— 10⁹³(94-digit number)
37628241573808988540…65789523259793726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.525 Γ— 10⁹³(94-digit number)
75256483147617977080…31579046519587453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.505 Γ— 10⁹⁴(95-digit number)
15051296629523595416…63158093039174906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.010 Γ— 10⁹⁴(95-digit number)
30102593259047190832…26316186078349813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.020 Γ— 10⁹⁴(95-digit number)
60205186518094381664…52632372156699627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.204 Γ— 10⁹⁡(96-digit number)
12041037303618876332…05264744313399255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.408 Γ— 10⁹⁡(96-digit number)
24082074607237752665…10529488626798510081
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:57,671,602 XPMΒ·at block #6,803,446 Β· updates every 60s
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