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Block #2,861,276

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/30/2018, 1:45:41 PM Β· Difficulty 11.6741 Β· 3,980,750 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6c61458101d2dc5d76e310b841f3003a181c416cd74e942d019efab86b973bae
View on Chainz β†—

Height

#2,861,276

Difficulty

11.674110

Transactions

1

Size

199 B

Version

2

Bits

0bac9272

Nonce

1,977,982,821

Timestamp

9/30/2018, 1:45:41 PM

Confirmations

3,980,750

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

33c30d78b0091135ccc1633ebf19559b9c86eb496354a0b0f80a9cc198e037cf
Transactions (1)
Coinbase33c30d78b00911…0a9cc198e037cf
1 in β†’ 1 out7.3300 XPM109 B
AUMQRepm…tAfKmdW1
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.

1.347 Γ— 10⁹⁴(95-digit number)
13473882920206420164…61874147542780451839
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
1.347 Γ— 10⁹⁴(95-digit number)
13473882920206420164…61874147542780451839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.694 Γ— 10⁹⁴(95-digit number)
26947765840412840328…23748295085560903679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.389 Γ— 10⁹⁴(95-digit number)
53895531680825680656…47496590171121807359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.077 Γ— 10⁹⁡(96-digit number)
10779106336165136131…94993180342243614719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.155 Γ— 10⁹⁡(96-digit number)
21558212672330272262…89986360684487229439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.311 Γ— 10⁹⁡(96-digit number)
43116425344660544525…79972721368974458879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.623 Γ— 10⁹⁡(96-digit number)
86232850689321089050…59945442737948917759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.724 Γ— 10⁹⁢(97-digit number)
17246570137864217810…19890885475897835519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.449 Γ— 10⁹⁢(97-digit number)
34493140275728435620…39781770951795671039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.898 Γ— 10⁹⁢(97-digit number)
68986280551456871240…79563541903591342079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.379 Γ— 10⁹⁷(98-digit number)
13797256110291374248…59127083807182684159
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:57,980,594 XPMΒ·at block #6,842,025 Β· updates every 60s
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