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Block #2,806,977

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/23/2018, 8:42:22 PM Β· Difficulty 11.6723 Β· 4,034,370 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f9e8fc67834ee55d280a6bec92dbb154d8c3c2c0ad11f65d4928a5f49fa04d9a
View on Chainz β†—

Height

#2,806,977

Difficulty

11.672308

Transactions

1

Size

200 B

Version

2

Bits

0bac1c67

Nonce

102,347,701

Timestamp

8/23/2018, 8:42:22 PM

Confirmations

4,034,370

Mined by

⛏️ P2SHAdKWoqURTN4ZEc5nX2FtJMhK3pqBpA2K7P

Merkle Root

acac08adde635d511e753716671d784eec1b4156f0b79f253965966ea0a24b34
Transactions (1)
Coinbaseacac08adde635d…65966ea0a24b34
1 in β†’ 1 out7.3300 XPM110 B
AdKWoqUR…qBpA2K7P
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.

2.820 Γ— 10⁹³(94-digit number)
28209126567033311572…54888657560461439499
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
2.820 Γ— 10⁹³(94-digit number)
28209126567033311572…54888657560461439499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.641 Γ— 10⁹³(94-digit number)
56418253134066623145…09777315120922878999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁴(95-digit number)
11283650626813324629…19554630241845757999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.256 Γ— 10⁹⁴(95-digit number)
22567301253626649258…39109260483691515999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.513 Γ— 10⁹⁴(95-digit number)
45134602507253298516…78218520967383031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.026 Γ— 10⁹⁴(95-digit number)
90269205014506597032…56437041934766063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.805 Γ— 10⁹⁡(96-digit number)
18053841002901319406…12874083869532127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.610 Γ— 10⁹⁡(96-digit number)
36107682005802638812…25748167739064255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.221 Γ— 10⁹⁡(96-digit number)
72215364011605277625…51496335478128511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.444 Γ— 10⁹⁢(97-digit number)
14443072802321055525…02992670956257023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.888 Γ— 10⁹⁢(97-digit number)
28886145604642111050…05985341912514047999
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:57,975,143 XPMΒ·at block #6,841,346 Β· updates every 60s
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