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Block #251,183

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 9:22:46 PM Β· Difficulty 9.9696 Β· 6,550,372 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01bbd7ac1e2113f635a7de22b3b90dc07964e4dac1e687c20832aa47ca468a36
View on Chainz β†—

Height

#251,183

Difficulty

9.969575

Transactions

1

Size

206 B

Version

2

Bits

09f83613

Nonce

819,879

Timestamp

11/8/2013, 9:22:46 PM

Confirmations

6,550,372

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

23e16cb6b511c146f9226d82270d513f4c3d46418891cd6e52a28b37089df297
Transactions (1)
Coinbase23e16cb6b511c1…a28b37089df297
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.595 Γ— 10⁹⁡(96-digit number)
25950885410641403301…45208644321220813441
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
2.595 Γ— 10⁹⁡(96-digit number)
25950885410641403301…45208644321220813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.190 Γ— 10⁹⁡(96-digit number)
51901770821282806603…90417288642441626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.038 Γ— 10⁹⁢(97-digit number)
10380354164256561320…80834577284883253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.076 Γ— 10⁹⁢(97-digit number)
20760708328513122641…61669154569766507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.152 Γ— 10⁹⁢(97-digit number)
41521416657026245283…23338309139533015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.304 Γ— 10⁹⁢(97-digit number)
83042833314052490566…46676618279066030081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.660 Γ— 10⁹⁷(98-digit number)
16608566662810498113…93353236558132060161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.321 Γ— 10⁹⁷(98-digit number)
33217133325620996226…86706473116264120321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.643 Γ— 10⁹⁷(98-digit number)
66434266651241992452…73412946232528240641
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:57,656,520 XPMΒ·at block #6,801,554 Β· updates every 60s
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