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Block #2,880,275

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/14/2018, 4:20:58 AM Β· Difficulty 11.6339 Β· 3,961,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ceb2e2b2f3e88ca05c81af3ce57c75f2aa921cdc0b86ec27b4a318fb3f9bbf8b
View on Chainz β†—

Height

#2,880,275

Difficulty

11.633857

Transactions

1

Size

200 B

Version

2

Bits

0ba24476

Nonce

1,421,897,940

Timestamp

10/14/2018, 4:20:58 AM

Confirmations

3,961,874

Mined by

⛏️ P2SHAb72Q5oxpAuqrjBA8w185CDpjqjs5iZrDn

Merkle Root

4106a99c3e2f019e122f6c323fdd5c67d67179c7d4e2795772818873bc846875
Transactions (1)
Coinbase4106a99c3e2f01…818873bc846875
1 in β†’ 1 out7.3800 XPM110 B
Ab72Q5ox…js5iZrDn
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.

7.008 Γ— 10⁹⁴(95-digit number)
70081588939478531810…82873287818212617291
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
7.008 Γ— 10⁹⁴(95-digit number)
70081588939478531810…82873287818212617291
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.401 Γ— 10⁹⁡(96-digit number)
14016317787895706362…65746575636425234581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.803 Γ— 10⁹⁡(96-digit number)
28032635575791412724…31493151272850469161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.606 Γ— 10⁹⁡(96-digit number)
56065271151582825448…62986302545700938321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.121 Γ— 10⁹⁢(97-digit number)
11213054230316565089…25972605091401876641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.242 Γ— 10⁹⁢(97-digit number)
22426108460633130179…51945210182803753281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.485 Γ— 10⁹⁢(97-digit number)
44852216921266260358…03890420365607506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.970 Γ— 10⁹⁢(97-digit number)
89704433842532520716…07780840731215013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.794 Γ— 10⁹⁷(98-digit number)
17940886768506504143…15561681462430026241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.588 Γ— 10⁹⁷(98-digit number)
35881773537013008286…31123362924860052481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.176 Γ— 10⁹⁷(98-digit number)
71763547074026016573…62246725849720104961
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,981,581 XPMΒ·at block #6,842,148 Β· updates every 60s
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