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Block #169,020

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/17/2013, 5:11:16 PM Β· Difficulty 9.8683 Β· 6,625,982 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b40bc0bc529fc1d768a769b0008c8280fbd2da8ed7d293dc15bb06e34fe81943
View on Chainz β†—

Height

#169,020

Difficulty

9.868334

Transactions

1

Size

198 B

Version

2

Bits

09de4b2a

Nonce

256,067

Timestamp

9/17/2013, 5:11:16 PM

Confirmations

6,625,982

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

4b802e0d92dfdbcfa7198d518009e0e377d903a03d6c5bd82c7b5ecfcb8b2a2c
Transactions (1)
Coinbase4b802e0d92dfdb…7b5ecfcb8b2a2c
1 in β†’ 1 out10.2500 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

1.610 Γ— 10⁹³(94-digit number)
16107786453138695845…36975333933786465751
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
1.610 Γ— 10⁹³(94-digit number)
16107786453138695845…36975333933786465751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.221 Γ— 10⁹³(94-digit number)
32215572906277391690…73950667867572931501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.443 Γ— 10⁹³(94-digit number)
64431145812554783380…47901335735145863001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.288 Γ— 10⁹⁴(95-digit number)
12886229162510956676…95802671470291726001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.577 Γ— 10⁹⁴(95-digit number)
25772458325021913352…91605342940583452001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.154 Γ— 10⁹⁴(95-digit number)
51544916650043826704…83210685881166904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.030 Γ— 10⁹⁡(96-digit number)
10308983330008765340…66421371762333808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.061 Γ— 10⁹⁡(96-digit number)
20617966660017530681…32842743524667616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.123 Γ— 10⁹⁡(96-digit number)
41235933320035061363…65685487049335232001
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:57,604,059 XPMΒ·at block #6,795,001 Β· updates every 60s
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