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Block #57,092

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 12:14:23 PM Β· Difficulty 8.9526 Β· 6,767,681 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42a7ac143060cbae277e7c7dcbf562866dcc9623ae70d9824f6d44e44ccd4b3d
View on Chainz β†—

Height

#57,092

Difficulty

8.952587

Transactions

1

Size

199 B

Version

2

Bits

08f3dcc1

Nonce

10

Timestamp

7/17/2013, 12:14:23 PM

Confirmations

6,767,681

Mined by

⛏️ P2SHAcuRhoVunZmd7TM7Neh2VRFvWv6Pu86km9

Merkle Root

481adffdf465ea3c77be7df322a2e56975b55d3f181abe168594e174cc927aa0
Transactions (1)
Coinbase481adffdf465ea…94e174cc927aa0
1 in β†’ 1 out12.4600 XPM110 B
AcuRhoVu…6Pu86km9
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.

4.726 Γ— 10⁹²(93-digit number)
47263813963389077852…75730027798541428179
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
4.726 Γ— 10⁹²(93-digit number)
47263813963389077852…75730027798541428179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.452 Γ— 10⁹²(93-digit number)
94527627926778155705…51460055597082856359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.890 Γ— 10⁹³(94-digit number)
18905525585355631141…02920111194165712719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.781 Γ— 10⁹³(94-digit number)
37811051170711262282…05840222388331425439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.562 Γ— 10⁹³(94-digit number)
75622102341422524564…11680444776662850879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁴(95-digit number)
15124420468284504912…23360889553325701759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.024 Γ— 10⁹⁴(95-digit number)
30248840936569009825…46721779106651403519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.049 Γ— 10⁹⁴(95-digit number)
60497681873138019651…93443558213302807039
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:57,842,256 XPMΒ·at block #6,824,772 Β· updates every 60s
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