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Block #261,812

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2013, 4:41:39 AM Β· Difficulty 9.9706 Β· 6,553,328 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e24bd9cc4fefb39cd96043b47f351ca9613fd66661ea0b7b04c53959abafb42
View on Chainz β†—

Height

#261,812

Difficulty

9.970628

Transactions

2

Size

1016 B

Version

2

Bits

09f87b16

Nonce

363,631

Timestamp

11/16/2013, 4:41:39 AM

Confirmations

6,553,328

Mined by

⛏️ P2SHAaeuUzM6yg517oE6cDQkAZUe7mWU19QiEe

Merkle Root

720745cf5396497d97d83e0130a21f8c63c249a64e20049c2a88c6dc765fe268
Transactions (2)
Coinbasefd095c4b481413…69b47828ead45c
1 in β†’ 1 out10.0500 XPM109 B
AaeuUzM6…WU19QiEe
d4e56c4aca742d…93e8cf2bc35562
5 in β†’ 2 out4.3161 XPM818 B
AM4d7iB1…oH9fGxioAHFCEs3o…Pbs9VA6g
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.

6.019 Γ— 10⁹²(93-digit number)
60198545165622580274…80155818343475767501
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
6.019 Γ— 10⁹²(93-digit number)
60198545165622580274…80155818343475767501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.203 Γ— 10⁹³(94-digit number)
12039709033124516054…60311636686951535001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.407 Γ— 10⁹³(94-digit number)
24079418066249032109…20623273373903070001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.815 Γ— 10⁹³(94-digit number)
48158836132498064219…41246546747806140001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.631 Γ— 10⁹³(94-digit number)
96317672264996128439…82493093495612280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.926 Γ— 10⁹⁴(95-digit number)
19263534452999225687…64986186991224560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.852 Γ— 10⁹⁴(95-digit number)
38527068905998451375…29972373982449120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.705 Γ— 10⁹⁴(95-digit number)
77054137811996902751…59944747964898240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.541 Γ— 10⁹⁡(96-digit number)
15410827562399380550…19889495929796480001
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:57,765,214 XPMΒ·at block #6,815,139 Β· updates every 60s
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