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Block #51,793

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 7:26:42 AM Β· Difficulty 8.9035 Β· 6,758,130 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df02df43769e4255e2fb6c055ca33807674c623c159847c8980be3cf28cd6920
View on Chainz β†—

Height

#51,793

Difficulty

8.903471

Transactions

1

Size

200 B

Version

2

Bits

08e749dc

Nonce

133

Timestamp

7/16/2013, 7:26:42 AM

Confirmations

6,758,130

Mined by

⛏️ P2SHAUE4zwpjLCmzQKECpmtvVXQKVNL2Q5BsyG

Merkle Root

50164bbfd7afc7cbd42aa0a675fa6ac5c48eae10506a217616b932fd74b75809
Transactions (1)
Coinbase50164bbfd7afc7…b932fd74b75809
1 in β†’ 1 out12.6000 XPM110 B
AUE4zwpj…L2Q5BsyG
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.

6.788 Γ— 10⁹⁴(95-digit number)
67886193794773661126…22593606953117779191
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
6.788 Γ— 10⁹⁴(95-digit number)
67886193794773661126…22593606953117779191
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.357 Γ— 10⁹⁡(96-digit number)
13577238758954732225…45187213906235558381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.715 Γ— 10⁹⁡(96-digit number)
27154477517909464450…90374427812471116761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.430 Γ— 10⁹⁡(96-digit number)
54308955035818928901…80748855624942233521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.086 Γ— 10⁹⁢(97-digit number)
10861791007163785780…61497711249884467041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.172 Γ— 10⁹⁢(97-digit number)
21723582014327571560…22995422499768934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.344 Γ— 10⁹⁢(97-digit number)
43447164028655143121…45990844999537868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.689 Γ— 10⁹⁢(97-digit number)
86894328057310286242…91981689999075736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.737 Γ— 10⁹⁷(98-digit number)
17378865611462057248…83963379998151472641
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:57,723,470 XPMΒ·at block #6,809,922 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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