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Block #2,857,920

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/28/2018, 3:42:29 AM Β· Difficulty 11.6823 Β· 3,975,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca7b64785e241edae3a2ea174c6fe3b82bd5a539d480c4eb2ca9364f08b5c18e
View on Chainz β†—

Height

#2,857,920

Difficulty

11.682283

Transactions

2

Size

422 B

Version

2

Bits

0baeaa1b

Nonce

936,880,934

Timestamp

9/28/2018, 3:42:29 AM

Confirmations

3,975,876

Mined by

⛏️ P2SHAeVqBcJ1X27ADxmorf2aZRzQGUReeQNdrS

Merkle Root

abda136163295f91d0b5b4cf3e8eb4fc679680e223131f34c79adcf5cc7bf063
Transactions (2)
Coinbase2a92bede243305…dd8bbd22e44143
1 in β†’ 1 out7.3200 XPM110 B
AeVqBcJ1…ReeQNdrS
48d0c255a9535d…0691202561c70c
1 in β†’ 1 out527.9900 XPM223 B
AYykcwb7…HGGCt7Sw
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.

8.067 Γ— 10⁹²(93-digit number)
80675093760767215427…05164639786390638081
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
8.067 Γ— 10⁹²(93-digit number)
80675093760767215427…05164639786390638081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.613 Γ— 10⁹³(94-digit number)
16135018752153443085…10329279572781276161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.227 Γ— 10⁹³(94-digit number)
32270037504306886171…20658559145562552321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.454 Γ— 10⁹³(94-digit number)
64540075008613772342…41317118291125104641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.290 Γ— 10⁹⁴(95-digit number)
12908015001722754468…82634236582250209281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.581 Γ— 10⁹⁴(95-digit number)
25816030003445508936…65268473164500418561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.163 Γ— 10⁹⁴(95-digit number)
51632060006891017873…30536946329000837121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.032 Γ— 10⁹⁡(96-digit number)
10326412001378203574…61073892658001674241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.065 Γ— 10⁹⁡(96-digit number)
20652824002756407149…22147785316003348481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.130 Γ— 10⁹⁡(96-digit number)
41305648005512814299…44295570632006696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.261 Γ— 10⁹⁡(96-digit number)
82611296011025628598…88591141264013393921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.652 Γ— 10⁹⁢(97-digit number)
16522259202205125719…77182282528026787841
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,914,589 XPMΒ·at block #6,833,795 Β· updates every 60s
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