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Block #2,779,604

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2018, 1:40:10 AM Β· Difficulty 11.6505 Β· 4,062,406 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97b723f90e617bdd75aefc7dbd31b76c6630f98afcae164c3058f6547de71578
View on Chainz β†—

Height

#2,779,604

Difficulty

11.650510

Transactions

2

Size

2.69 KB

Version

2

Bits

0ba687d6

Nonce

1,511,798,615

Timestamp

8/5/2018, 1:40:10 AM

Confirmations

4,062,406

Mined by

⛏️ P2SHAah665G8oCz5hg2Y11bFpG7xXm3eK7SW2G

Merkle Root

d1097872f8cc0eba184f6f6249d1f326b1efac41aec15d0a0457fa4392c2f0fb
Transactions (2)
Coinbase8b0d32413d5b51…686afc8cf81976
1 in β†’ 1 out7.3800 XPM110 B
Aah665G8…3eK7SW2G
b42bfc6b63cbe6…380fd21e02a725
17 in β†’ 1 out160.0000 XPM2.50 KB
ALh5G3Np…6TsNC2wj
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.

5.988 Γ— 10⁹⁴(95-digit number)
59881499147238008501…04308755641705021439
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
5.988 Γ— 10⁹⁴(95-digit number)
59881499147238008501…04308755641705021439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.197 Γ— 10⁹⁡(96-digit number)
11976299829447601700…08617511283410042879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.395 Γ— 10⁹⁡(96-digit number)
23952599658895203400…17235022566820085759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.790 Γ— 10⁹⁡(96-digit number)
47905199317790406801…34470045133640171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.581 Γ— 10⁹⁡(96-digit number)
95810398635580813602…68940090267280343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.916 Γ— 10⁹⁢(97-digit number)
19162079727116162720…37880180534560686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.832 Γ— 10⁹⁢(97-digit number)
38324159454232325440…75760361069121372159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.664 Γ— 10⁹⁢(97-digit number)
76648318908464650881…51520722138242744319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁷(98-digit number)
15329663781692930176…03041444276485488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.065 Γ— 10⁹⁷(98-digit number)
30659327563385860352…06082888552970977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.131 Γ— 10⁹⁷(98-digit number)
61318655126771720705…12165777105941954559
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:57,980,465 XPMΒ·at block #6,842,009 Β· updates every 60s
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