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Block #54,126

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 6:49:33 PM Β· Difficulty 8.9305 Β· 6,771,337 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de6964c736ff0b25b30e88e4ddb1f6ac85d5ca7fd9a5573f3044e5c918a6dbab
View on Chainz β†—

Height

#54,126

Difficulty

8.930481

Transactions

1

Size

197 B

Version

2

Bits

08ee33fa

Nonce

157

Timestamp

7/16/2013, 6:49:33 PM

Confirmations

6,771,337

Mined by

⛏️ P2SHAX85bWR1s13thBJxnmv7Zr62AvX2GwLbPj

Merkle Root

f070e8c73dd504b64e6d4529c5fc452b20bab4dede6b1ad38a9763477ff48b59
Transactions (1)
Coinbasef070e8c73dd504…9763477ff48b59
1 in β†’ 1 out12.5200 XPM110 B
AX85bWR1…X2GwLbPj
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.

2.943 Γ— 10⁸⁷(88-digit number)
29434081936568995328…54478793977804748001
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
2.943 Γ— 10⁸⁷(88-digit number)
29434081936568995328…54478793977804748001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.886 Γ— 10⁸⁷(88-digit number)
58868163873137990657…08957587955609496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.177 Γ— 10⁸⁸(89-digit number)
11773632774627598131…17915175911218992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.354 Γ— 10⁸⁸(89-digit number)
23547265549255196262…35830351822437984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.709 Γ— 10⁸⁸(89-digit number)
47094531098510392525…71660703644875968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.418 Γ— 10⁸⁸(89-digit number)
94189062197020785051…43321407289751936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.883 Γ— 10⁸⁹(90-digit number)
18837812439404157010…86642814579503872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.767 Γ— 10⁸⁹(90-digit number)
37675624878808314020…73285629159007744001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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
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