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Block #297,170

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/6/2013, 11:11:18 AM Β· Difficulty 9.9919 Β· 6,498,974 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fa326ea334ce554a27798ae3bce5251160633dc5c5a26d697db428d087d468e9
View on Chainz β†—

Height

#297,170

Difficulty

9.991883

Transactions

2

Size

1017 B

Version

2

Bits

09fdec09

Nonce

25,811

Timestamp

12/6/2013, 11:11:18 AM

Confirmations

6,498,974

Mined by

⛏️ P2SHAWAj7do2FZbvhho4ktsT4Kwg1jdGqV5dgd

Merkle Root

e50fab435b1fa974b159368b84b93a4ac1185acdbf5971331da6b31868ce534c
Transactions (2)
Coinbase72eb613e9d0833…0f524d79265ceb
1 in β†’ 1 out10.0200 XPM109 B
AWAj7do2…dGqV5dgd
7d909b074610f4…3c0613b75499c5
5 in β†’ 2 out454.1600 XPM818 B
AJnA7nsr…Y7MNquJtAUt2sZ1k…BPWs8HRi
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.

9.782 Γ— 10⁹⁴(95-digit number)
97826027158943844296…68102576141422643201
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
9.782 Γ— 10⁹⁴(95-digit number)
97826027158943844296…68102576141422643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.956 Γ— 10⁹⁡(96-digit number)
19565205431788768859…36205152282845286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.913 Γ— 10⁹⁡(96-digit number)
39130410863577537718…72410304565690572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.826 Γ— 10⁹⁡(96-digit number)
78260821727155075436…44820609131381145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.565 Γ— 10⁹⁢(97-digit number)
15652164345431015087…89641218262762291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.130 Γ— 10⁹⁢(97-digit number)
31304328690862030174…79282436525524582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.260 Γ— 10⁹⁢(97-digit number)
62608657381724060349…58564873051049164801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.252 Γ— 10⁹⁷(98-digit number)
12521731476344812069…17129746102098329601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.504 Γ— 10⁹⁷(98-digit number)
25043462952689624139…34259492204196659201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.008 Γ— 10⁹⁷(98-digit number)
50086925905379248279…68518984408393318401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,613,149 XPMΒ·at block #6,796,143 Β· updates every 60s
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