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Block #57,481

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 2:55:48 PM Β· Difficulty 8.9547 Β· 6,756,781 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77ef5a05d9582703bde9dfa69dc427c3cde20e3f67c82665d49f4d6595ec6630
View on Chainz β†—

Height

#57,481

Difficulty

8.954697

Transactions

1

Size

200 B

Version

2

Bits

08f466fe

Nonce

459

Timestamp

7/17/2013, 2:55:48 PM

Confirmations

6,756,781

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

1afa54ebc47406821859d89a5f26817aecb5b0bf25489e33998653d25bda6668
Transactions (1)
Coinbase1afa54ebc47406…8653d25bda6668
1 in β†’ 1 out12.4500 XPM110 B
ALXjrugC…hByoynjy
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.

4.369 Γ— 10⁹⁴(95-digit number)
43699825692970286926…91404987601693454079
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.369 Γ— 10⁹⁴(95-digit number)
43699825692970286926…91404987601693454079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.739 Γ— 10⁹⁴(95-digit number)
87399651385940573853…82809975203386908159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.747 Γ— 10⁹⁡(96-digit number)
17479930277188114770…65619950406773816319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.495 Γ— 10⁹⁡(96-digit number)
34959860554376229541…31239900813547632639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.991 Γ— 10⁹⁡(96-digit number)
69919721108752459082…62479801627095265279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.398 Γ— 10⁹⁢(97-digit number)
13983944221750491816…24959603254190530559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.796 Γ— 10⁹⁢(97-digit number)
27967888443500983633…49919206508381061119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.593 Γ— 10⁹⁢(97-digit number)
55935776887001967266…99838413016762122239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,758,163 XPMΒ·at block #6,814,261 Β· updates every 60s
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