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Block #150,182

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 8:39:07 PM Β· Difficulty 9.8588 Β· 6,656,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4de1c4c61d480f672a5dce6fa00eb0f1c35b2a33a163d33cb543cb8381352f26
View on Chainz β†—

Height

#150,182

Difficulty

9.858780

Transactions

1

Size

196 B

Version

2

Bits

09dbd908

Nonce

211,050

Timestamp

9/4/2013, 8:39:07 PM

Confirmations

6,656,503

Mined by

⛏️ P2SHAa6PpN3XWen9U28VLp3hDw33d6XAm9RHxt

Merkle Root

93269468dc28f1f311998cb222fa029cf549157c4b39eba2ac3eba449ab8c15b
Transactions (1)
Coinbase93269468dc28f1…3eba449ab8c15b
1 in β†’ 1 out10.2700 XPM109 B
Aa6PpN3X…XAm9RHxt
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.

2.109 Γ— 10⁸⁸(89-digit number)
21093664515307091468…89744691736296054751
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
2.109 Γ— 10⁸⁸(89-digit number)
21093664515307091468…89744691736296054751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.218 Γ— 10⁸⁸(89-digit number)
42187329030614182936…79489383472592109501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.437 Γ— 10⁸⁸(89-digit number)
84374658061228365872…58978766945184219001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.687 Γ— 10⁸⁹(90-digit number)
16874931612245673174…17957533890368438001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.374 Γ— 10⁸⁹(90-digit number)
33749863224491346348…35915067780736876001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.749 Γ— 10⁸⁹(90-digit number)
67499726448982692697…71830135561473752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.349 Γ— 10⁹⁰(91-digit number)
13499945289796538539…43660271122947504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.699 Γ— 10⁹⁰(91-digit number)
26999890579593077079…87320542245895008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.399 Γ— 10⁹⁰(91-digit number)
53999781159186154158…74641084491790016001
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:57,697,574 XPMΒ·at block #6,806,684 Β· updates every 60s
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