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Block #2,176,617

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/25/2017, 2:43:41 AM Β· Difficulty 10.9203 Β· 4,649,079 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a327b0e06ea3a5710c0dbc06fff319c85509df7fc12327c20b8ea3aff67119c
View on Chainz β†—

Height

#2,176,617

Difficulty

10.920342

Transactions

1

Size

200 B

Version

2

Bits

0aeb9b8e

Nonce

269,753,871

Timestamp

6/25/2017, 2:43:41 AM

Confirmations

4,649,079

Mined by

⛏️ P2SHAH9Knvg2nuasGCXXPiuLpPzW9xZsHUyTbh

Merkle Root

fbbbcdee9c00640554e4fa3028739869579e2535aeeaf941f5c18774e9ad8847
Transactions (1)
Coinbasefbbbcdee9c0064…c18774e9ad8847
1 in β†’ 1 out8.3700 XPM110 B
AH9Knvg2…ZsHUyTbh
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.

2.235 Γ— 10⁹⁡(96-digit number)
22350059036260822380…98566138362874286241
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
2.235 Γ— 10⁹⁡(96-digit number)
22350059036260822380…98566138362874286241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.470 Γ— 10⁹⁡(96-digit number)
44700118072521644761…97132276725748572481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.940 Γ— 10⁹⁡(96-digit number)
89400236145043289523…94264553451497144961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.788 Γ— 10⁹⁢(97-digit number)
17880047229008657904…88529106902994289921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.576 Γ— 10⁹⁢(97-digit number)
35760094458017315809…77058213805988579841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.152 Γ— 10⁹⁢(97-digit number)
71520188916034631618…54116427611977159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.430 Γ— 10⁹⁷(98-digit number)
14304037783206926323…08232855223954319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.860 Γ— 10⁹⁷(98-digit number)
28608075566413852647…16465710447908638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.721 Γ— 10⁹⁷(98-digit number)
57216151132827705294…32931420895817277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.144 Γ— 10⁹⁸(99-digit number)
11443230226565541058…65862841791634554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.288 Γ— 10⁹⁸(99-digit number)
22886460453131082117…31725683583269109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
4.577 Γ— 10⁹⁸(99-digit number)
45772920906262164235…63451367166538219521
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,849,680 XPMΒ·at block #6,825,695 Β· updates every 60s
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