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Block #167,867

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2013, 10:02:20 PM Β· Difficulty 9.8682 Β· 6,639,841 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e126188de9149cbea9ed1d5eca4a3153fd14082229ba29c6aa7729814ecf2161
View on Chainz β†—

Height

#167,867

Difficulty

9.868165

Transactions

1

Size

198 B

Version

2

Bits

09de400c

Nonce

56,789

Timestamp

9/16/2013, 10:02:20 PM

Confirmations

6,639,841

Mined by

⛏️ P2SHAbuNadfrJKrPdSqunS7mp7gfv5b1PyHGcf

Merkle Root

542289bc44d9067d94e8fd809af5fec771f34ac92bc14c67542e3f00408fab2c
Transactions (1)
Coinbase542289bc44d906…2e3f00408fab2c
1 in β†’ 1 out10.2500 XPM109 B
AbuNadfr…b1PyHGcf
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.

4.390 Γ— 10⁹²(93-digit number)
43901087339183600155…76089552087671923121
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
4.390 Γ— 10⁹²(93-digit number)
43901087339183600155…76089552087671923121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.780 Γ— 10⁹²(93-digit number)
87802174678367200310…52179104175343846241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.756 Γ— 10⁹³(94-digit number)
17560434935673440062…04358208350687692481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.512 Γ— 10⁹³(94-digit number)
35120869871346880124…08716416701375384961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.024 Γ— 10⁹³(94-digit number)
70241739742693760248…17432833402750769921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.404 Γ— 10⁹⁴(95-digit number)
14048347948538752049…34865666805501539841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.809 Γ— 10⁹⁴(95-digit number)
28096695897077504099…69731333611003079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.619 Γ— 10⁹⁴(95-digit number)
56193391794155008198…39462667222006159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.123 Γ— 10⁹⁡(96-digit number)
11238678358831001639…78925334444012318721
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:57,705,695 XPMΒ·at block #6,807,707 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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