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Block #2,830,210

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2018, 12:12:28 PM Β· Difficulty 11.7157 Β· 4,015,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f6aefd36913528f52a12f048975fd73030fd04fecf3011cbd1941d306c511a60
View on Chainz β†—

Height

#2,830,210

Difficulty

11.715657

Transactions

1

Size

200 B

Version

2

Bits

0bb73551

Nonce

1,030,515,573

Timestamp

9/8/2018, 12:12:28 PM

Confirmations

4,015,166

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

bb2e46c8a30d9a453cd4c44b568d32c3ca59daa966b088d7bec8ee8cd4bdd982
Transactions (1)
Coinbasebb2e46c8a30d9a…c8ee8cd4bdd982
1 in β†’ 1 out7.2700 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.021 Γ— 10⁹⁴(95-digit number)
50215096041786180959…07123740680043283199
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
5.021 Γ— 10⁹⁴(95-digit number)
50215096041786180959…07123740680043283199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁡(96-digit number)
10043019208357236191…14247481360086566399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.008 Γ— 10⁹⁡(96-digit number)
20086038416714472383…28494962720173132799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.017 Γ— 10⁹⁡(96-digit number)
40172076833428944767…56989925440346265599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.034 Γ— 10⁹⁡(96-digit number)
80344153666857889535…13979850880692531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.606 Γ— 10⁹⁢(97-digit number)
16068830733371577907…27959701761385062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.213 Γ— 10⁹⁢(97-digit number)
32137661466743155814…55919403522770124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.427 Γ— 10⁹⁢(97-digit number)
64275322933486311628…11838807045540249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁷(98-digit number)
12855064586697262325…23677614091080499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁷(98-digit number)
25710129173394524651…47355228182160998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.142 Γ— 10⁹⁷(98-digit number)
51420258346789049302…94710456364321996799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,007,452 XPMΒ·at block #6,845,375 Β· updates every 60s
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