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Block #2,697,298

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/8/2018, 7:45:09 PM Β· Difficulty 11.6566 Β· 4,136,662 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
28bcc0c9da6aacdee0d5e1d285845f7d0cb6be9b49ebef94a1b5e60c9d86f40a
View on Chainz β†—

Height

#2,697,298

Difficulty

11.656628

Transactions

2

Size

723 B

Version

2

Bits

0ba818c5

Nonce

889,518,461

Timestamp

6/8/2018, 7:45:09 PM

Confirmations

4,136,662

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e2e64e4d4a71e4b9228fbbd265832c5d830ab243928adada97b0e0bf620fa27c
Transactions (2)
Coinbase765f302eabb517…95e1d7e4bc336d
1 in β†’ 1 out7.3600 XPM110 B
Adqah8zh…1WwoHJ9t
c8d7bff33a9750…0ab1af04bcdcbc
3 in β†’ 2 out11.2200 XPM523 B
Adjbb1hx…21KVAEZVAHqFbYDw…87iqm3ic
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.

6.738 Γ— 10⁹⁴(95-digit number)
67384919001834766343…80351758001057398651
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
6.738 Γ— 10⁹⁴(95-digit number)
67384919001834766343…80351758001057398651
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.347 Γ— 10⁹⁡(96-digit number)
13476983800366953268…60703516002114797301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.695 Γ— 10⁹⁡(96-digit number)
26953967600733906537…21407032004229594601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.390 Γ— 10⁹⁡(96-digit number)
53907935201467813075…42814064008459189201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.078 Γ— 10⁹⁢(97-digit number)
10781587040293562615…85628128016918378401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.156 Γ— 10⁹⁢(97-digit number)
21563174080587125230…71256256033836756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.312 Γ— 10⁹⁢(97-digit number)
43126348161174250460…42512512067673513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.625 Γ— 10⁹⁢(97-digit number)
86252696322348500920…85025024135347027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.725 Γ— 10⁹⁷(98-digit number)
17250539264469700184…70050048270694054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.450 Γ— 10⁹⁷(98-digit number)
34501078528939400368…40100096541388108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.900 Γ— 10⁹⁷(98-digit number)
69002157057878800736…80200193082776217601
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:57,915,908 XPMΒ·at block #6,833,959 Β· updates every 60s
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