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Block #432,968

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2014, 7:04:24 AM Β· Difficulty 10.3395 Β· 6,374,171 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1b9326eacc0aa9e85eb0df5c2bf9f401d6afff1f02ce79cff6fd69739e9e877
View on Chainz β†—

Height

#432,968

Difficulty

10.339535

Transactions

2

Size

413 B

Version

2

Bits

0a56ebbf

Nonce

24,640

Timestamp

3/7/2014, 7:04:24 AM

Confirmations

6,374,171

Mined by

⛏️ HaSnAbMAHMS8edmSw9jhkJ2fCCZzvKMwEzMSoj

Merkle Root

95165745c0fb1cb621bee1eac2f26188b95ed9fd103507c58e92cbce3ec662c3
Transactions (2)
Coinbase68aa963f917cd2…2bb13b8b7be46b
1 in β†’ 1 out9.3400 XPM97 B
AbMAHMS8…MwEzMSoj
b8581e35030d40…7deba9b854ae5d
1 in β†’ 2 out1.0109 XPM226 B
AV3q2AB3…nVr27xYPAdNBYnmC…mEtS6md8
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.

2.434 Γ— 10⁹⁡(96-digit number)
24349396033966425437…84292641301043887361
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
2.434 Γ— 10⁹⁡(96-digit number)
24349396033966425437…84292641301043887361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.869 Γ— 10⁹⁡(96-digit number)
48698792067932850874…68585282602087774721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.739 Γ— 10⁹⁡(96-digit number)
97397584135865701748…37170565204175549441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.947 Γ— 10⁹⁢(97-digit number)
19479516827173140349…74341130408351098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.895 Γ— 10⁹⁢(97-digit number)
38959033654346280699…48682260816702197761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.791 Γ— 10⁹⁢(97-digit number)
77918067308692561398…97364521633404395521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.558 Γ— 10⁹⁷(98-digit number)
15583613461738512279…94729043266808791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.116 Γ— 10⁹⁷(98-digit number)
31167226923477024559…89458086533617582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.233 Γ— 10⁹⁷(98-digit number)
62334453846954049119…78916173067235164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.246 Γ— 10⁹⁸(99-digit number)
12466890769390809823…57832346134470328321
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:57,701,119 XPMΒ·at block #6,807,138 Β· updates every 60s
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