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Block #2,867,988

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/5/2018, 7:16:31 AM Β· Difficulty 11.6678 Β· 3,974,768 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1285fd461c99c5bcf98b59ac138adf25856510d92d9f5410be2d0d375b3b2596
View on Chainz β†—

Height

#2,867,988

Difficulty

11.667826

Transactions

1

Size

200 B

Version

2

Bits

0baaf69f

Nonce

1,169,960,089

Timestamp

10/5/2018, 7:16:31 AM

Confirmations

3,974,768

Mined by

⛏️ P2SHAVAb2WFjvZuhHR8eT9WAwHYqmpadk4F38g

Merkle Root

05dcdd8936ce2509a396079dc99720918c70bac8fe3de26f5d23f4d8a4fde146
Transactions (1)
Coinbase05dcdd8936ce25…23f4d8a4fde146
1 in β†’ 1 out7.3300 XPM109 B
AVAb2WFj…adk4F38g
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.

4.321 Γ— 10⁹⁢(97-digit number)
43213958094481185312…94895975389333012479
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
4.321 Γ— 10⁹⁢(97-digit number)
43213958094481185312…94895975389333012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.642 Γ— 10⁹⁢(97-digit number)
86427916188962370625…89791950778666024959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁷(98-digit number)
17285583237792474125…79583901557332049919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.457 Γ— 10⁹⁷(98-digit number)
34571166475584948250…59167803114664099839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.914 Γ— 10⁹⁷(98-digit number)
69142332951169896500…18335606229328199679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁸(99-digit number)
13828466590233979300…36671212458656399359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁸(99-digit number)
27656933180467958600…73342424917312798719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.531 Γ— 10⁹⁸(99-digit number)
55313866360935917200…46684849834625597439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁹(100-digit number)
11062773272187183440…93369699669251194879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁹(100-digit number)
22125546544374366880…86739399338502389759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.425 Γ— 10⁹⁹(100-digit number)
44251093088748733760…73478798677004779519
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:57,986,385 XPMΒ·at block #6,842,755 Β· updates every 60s
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