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Block #1,166,266

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2015, 4:06:52 AM Β· Difficulty 10.9341 Β· 5,644,542 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e40833e3582d61069f938d1867d05bc60221a5f7abf8e439f7fb056bd737d78
View on Chainz β†—

Height

#1,166,266

Difficulty

10.934101

Transactions

2

Size

94.39 KB

Version

2

Bits

0aef213f

Nonce

2,096,626,403

Timestamp

7/23/2015, 4:06:52 AM

Confirmations

5,644,542

Mined by

⛏️ P2SHAaNX8pn6Um2Pq1co1d7isy1MdVsuJJdX1z

Merkle Root

d5dd65866a02faef4e117ef3dfb9504c2af8569b73aaf6e03baa3cbfa60be3bc
Transactions (2)
Coinbasee9dfe26d24e7b6…715ef8a91bc0d2
1 in β†’ 1 out9.3200 XPM110 B
AaNX8pn6…suJJdX1z
5c0466f678ed46…a9e507c7cb8900
651 in β†’ 2 out900.0100 XPM94.19 KB
ANhhjWL2…1SpsZZTWAYKArr5V…V9VqiqCZ
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.

9.711 Γ— 10⁹²(93-digit number)
97113177669561990505…81166622883704831041
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
9.711 Γ— 10⁹²(93-digit number)
97113177669561990505…81166622883704831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.942 Γ— 10⁹³(94-digit number)
19422635533912398101…62333245767409662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.884 Γ— 10⁹³(94-digit number)
38845271067824796202…24666491534819324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.769 Γ— 10⁹³(94-digit number)
77690542135649592404…49332983069638648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.553 Γ— 10⁹⁴(95-digit number)
15538108427129918480…98665966139277296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.107 Γ— 10⁹⁴(95-digit number)
31076216854259836961…97331932278554593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.215 Γ— 10⁹⁴(95-digit number)
62152433708519673923…94663864557109186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.243 Γ— 10⁹⁡(96-digit number)
12430486741703934784…89327729114218373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.486 Γ— 10⁹⁡(96-digit number)
24860973483407869569…78655458228436746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.972 Γ— 10⁹⁡(96-digit number)
49721946966815739138…57310916456873492481
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:57,730,564 XPMΒ·at block #6,810,807 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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