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Block #2,633,521

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 11:50:46 AM Β· Difficulty 11.1947 Β· 4,208,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b97b6e69935633b770c73946e59506e86c5204d7f6831d041e61bc8bef9a3d67
View on Chainz β†—

Height

#2,633,521

Difficulty

11.194665

Transactions

2

Size

573 B

Version

2

Bits

0b31d589

Nonce

151,531,414

Timestamp

4/28/2018, 11:50:46 AM

Confirmations

4,208,166

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

245d4e7be86053623ce4b9ed2c2512f1f75dc9a19d2b3458927d6567f5131995
Transactions (2)
Coinbase8e67068749e37b…01ed9a417dfdce
1 in β†’ 1 out7.9800 XPM110 B
Adqah8zh…1WwoHJ9t
614b38425c4577…0b400308779cba
2 in β†’ 2 out107.1567 XPM373 B
AYJF7z3a…ZXfv75UEAMvpnbRe…TJShS8um
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.

1.094 Γ— 10⁹⁴(95-digit number)
10943635233613912996…84760945079855978039
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
1.094 Γ— 10⁹⁴(95-digit number)
10943635233613912996…84760945079855978039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.188 Γ— 10⁹⁴(95-digit number)
21887270467227825992…69521890159711956079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.377 Γ— 10⁹⁴(95-digit number)
43774540934455651985…39043780319423912159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.754 Γ— 10⁹⁴(95-digit number)
87549081868911303970…78087560638847824319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.750 Γ— 10⁹⁡(96-digit number)
17509816373782260794…56175121277695648639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.501 Γ— 10⁹⁡(96-digit number)
35019632747564521588…12350242555391297279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.003 Γ— 10⁹⁡(96-digit number)
70039265495129043176…24700485110782594559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.400 Γ— 10⁹⁢(97-digit number)
14007853099025808635…49400970221565189119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.801 Γ— 10⁹⁢(97-digit number)
28015706198051617270…98801940443130378239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.603 Γ— 10⁹⁢(97-digit number)
56031412396103234541…97603880886260756479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁷(98-digit number)
11206282479220646908…95207761772521512959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.241 Γ— 10⁹⁷(98-digit number)
22412564958441293816…90415523545043025919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,977,884 XPMΒ·at block #6,841,686 Β· updates every 60s
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