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Block #2,168,154

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/20/2017, 2:13:27 AM Β· Difficulty 10.8980 Β· 4,639,767 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b16c328bcdb26914c792610499383529025df682b8423916e395225c8383cca
View on Chainz β†—

Height

#2,168,154

Difficulty

10.897991

Transactions

2

Size

8.19 KB

Version

2

Bits

0ae5e2c0

Nonce

51,620,903

Timestamp

6/20/2017, 2:13:27 AM

Confirmations

4,639,767

Mined by

⛏️ P2SHAcMdK2SCepWjt5o3jd5wewHaHyn8tspxSY

Merkle Root

3c2e8d3528519768a3e52916fce24c5079fc56b119b518afd95ce5047b2de725
Transactions (2)
Coinbase2f9674d251e2fb…2d0e481eedb99c
1 in β†’ 1 out8.5200 XPM110 B
AcMdK2SC…n8tspxSY
db6a81191c1e36…9755ea2c43aa1c
55 in β†’ 1 out869.9900 XPM8.00 KB
AcxhUhX6…N8N8w2tm
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.

5.978 Γ— 10⁹²(93-digit number)
59786445220639269748…71344011061253652799
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
5.978 Γ— 10⁹²(93-digit number)
59786445220639269748…71344011061253652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.195 Γ— 10⁹³(94-digit number)
11957289044127853949…42688022122507305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.391 Γ— 10⁹³(94-digit number)
23914578088255707899…85376044245014611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.782 Γ— 10⁹³(94-digit number)
47829156176511415798…70752088490029222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.565 Γ— 10⁹³(94-digit number)
95658312353022831597…41504176980058444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.913 Γ— 10⁹⁴(95-digit number)
19131662470604566319…83008353960116889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.826 Γ— 10⁹⁴(95-digit number)
38263324941209132638…66016707920233779199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.652 Γ— 10⁹⁴(95-digit number)
76526649882418265277…32033415840467558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁡(96-digit number)
15305329976483653055…64066831680935116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.061 Γ— 10⁹⁡(96-digit number)
30610659952967306111…28133663361870233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.122 Γ— 10⁹⁡(96-digit number)
61221319905934612222…56267326723740467199
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:57,707,404 XPMΒ·at block #6,807,920 Β· updates every 60s
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