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Block #169,850

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2013, 8:00:50 AM Β· Difficulty 9.8669 Β· 6,638,249 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b5a32d7136c9e185fa9a9d52be35557faa6f36f6d686db30e4384106d3855261
View on Chainz β†—

Height

#169,850

Difficulty

9.866851

Transactions

1

Size

199 B

Version

2

Bits

09dde9ec

Nonce

458,442

Timestamp

9/18/2013, 8:00:50 AM

Confirmations

6,638,249

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

2100c1999aae5550bd7bb8a5fc8d7799d58bd05309f88af0dd4cecf1cc9b98f0
Transactions (1)
Coinbase2100c1999aae55…4cecf1cc9b98f0
1 in β†’ 1 out10.2600 XPM109 B
AUm1UXE6…STx2UrXW
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.

5.016 Γ— 10⁹³(94-digit number)
50160451396810095135…35560980750769542401
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
5.016 Γ— 10⁹³(94-digit number)
50160451396810095135…35560980750769542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.003 Γ— 10⁹⁴(95-digit number)
10032090279362019027…71121961501539084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.006 Γ— 10⁹⁴(95-digit number)
20064180558724038054…42243923003078169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.012 Γ— 10⁹⁴(95-digit number)
40128361117448076108…84487846006156339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.025 Γ— 10⁹⁴(95-digit number)
80256722234896152216…68975692012312678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.605 Γ— 10⁹⁡(96-digit number)
16051344446979230443…37951384024625356801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.210 Γ— 10⁹⁡(96-digit number)
32102688893958460886…75902768049250713601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.420 Γ— 10⁹⁡(96-digit number)
64205377787916921773…51805536098501427201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.284 Γ— 10⁹⁢(97-digit number)
12841075557583384354…03611072197002854401
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:57,708,837 XPMΒ·at block #6,808,098 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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