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Block #237,294

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 11:16:05 PM Β· Difficulty 9.9495 Β· 6,572,515 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
219a2f4f65456be84654289dbf2caa0336a6a7ed3a2a9318dbb52d6deb4edada
View on Chainz β†—

Height

#237,294

Difficulty

9.949478

Transactions

1

Size

200 B

Version

2

Bits

09f310f8

Nonce

235,272

Timestamp

10/31/2013, 11:16:05 PM

Confirmations

6,572,515

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

e5c8331a49171345aa339ea54f265e738181c6f9b305bbb2ec2578ecc0638af2
Transactions (1)
Coinbasee5c8331a491713…2578ecc0638af2
1 in β†’ 1 out10.0900 XPM109 B
AXbpyooS…bup7bQTH
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.

4.162 Γ— 10⁹⁷(98-digit number)
41621217043789479813…37220147566639794801
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
4.162 Γ— 10⁹⁷(98-digit number)
41621217043789479813…37220147566639794801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.324 Γ— 10⁹⁷(98-digit number)
83242434087578959627…74440295133279589601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.664 Γ— 10⁹⁸(99-digit number)
16648486817515791925…48880590266559179201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.329 Γ— 10⁹⁸(99-digit number)
33296973635031583850…97761180533118358401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.659 Γ— 10⁹⁸(99-digit number)
66593947270063167701…95522361066236716801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.331 Γ— 10⁹⁹(100-digit number)
13318789454012633540…91044722132473433601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.663 Γ— 10⁹⁹(100-digit number)
26637578908025267080…82089444264946867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.327 Γ— 10⁹⁹(100-digit number)
53275157816050534161…64178888529893734401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.065 Γ— 10¹⁰⁰(101-digit number)
10655031563210106832…28357777059787468801
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:57,722,554 XPMΒ·at block #6,809,808 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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