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Block #535,231

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2014, 7:21:41 PM Β· Difficulty 10.9041 Β· 6,261,054 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1c4b19aa0b6de3c3b9b6563c178dfe8286852a78d9cd9bddc107534b8661876a
View on Chainz β†—

Height

#535,231

Difficulty

10.904082

Transactions

2

Size

2.70 KB

Version

2

Bits

0ae771e3

Nonce

84,816,975

Timestamp

5/10/2014, 7:21:41 PM

Confirmations

6,261,054

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

78eb732461adfc88201a3904b5b994014eca065b79b0c84a6c633531dc5c9cbe
Transactions (2)
Coinbasea88941637555bd…2c7ce3efea7765
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
1c76ef9c92e630…c60e17aaab29bf
17 in β†’ 1 out51.0460 XPM2.50 KB
AYfGXBG3…s4uNnsy3
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.

6.423 Γ— 10⁹⁸(99-digit number)
64231747176216262629…69233994021057808961
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
6.423 Γ— 10⁹⁸(99-digit number)
64231747176216262629…69233994021057808961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.284 Γ— 10⁹⁹(100-digit number)
12846349435243252525…38467988042115617921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.569 Γ— 10⁹⁹(100-digit number)
25692698870486505051…76935976084231235841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.138 Γ— 10⁹⁹(100-digit number)
51385397740973010103…53871952168462471681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.027 Γ— 10¹⁰⁰(101-digit number)
10277079548194602020…07743904336924943361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.055 Γ— 10¹⁰⁰(101-digit number)
20554159096389204041…15487808673849886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.110 Γ— 10¹⁰⁰(101-digit number)
41108318192778408082…30975617347699773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.221 Γ— 10¹⁰⁰(101-digit number)
82216636385556816165…61951234695399546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.644 Γ— 10¹⁰¹(102-digit number)
16443327277111363233…23902469390799093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.288 Γ— 10¹⁰¹(102-digit number)
32886654554222726466…47804938781598187521
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:57,614,283 XPMΒ·at block #6,796,284 Β· updates every 60s
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