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Block #2,774,787

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/1/2018, 1:22:54 PM Β· Difficulty 11.6666 Β· 4,067,192 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
14ce652347c1e5090d8f84738637a584b231a4f1be04d609adc7d7cb1d4e1ab5
View on Chainz β†—

Height

#2,774,787

Difficulty

11.666589

Transactions

1

Size

200 B

Version

2

Bits

0baaa594

Nonce

650,328,426

Timestamp

8/1/2018, 1:22:54 PM

Confirmations

4,067,192

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

5d52bdcfd6b39cf58103e7b84f90e47bb89cd23142d9e6c2ff775b0daa9cbfdb
Transactions (1)
Coinbase5d52bdcfd6b39c…775b0daa9cbfdb
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

7.475 Γ— 10⁹⁴(95-digit number)
74757638052648091863…41309770318247356161
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
7.475 Γ— 10⁹⁴(95-digit number)
74757638052648091863…41309770318247356161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.495 Γ— 10⁹⁡(96-digit number)
14951527610529618372…82619540636494712321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.990 Γ— 10⁹⁡(96-digit number)
29903055221059236745…65239081272989424641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.980 Γ— 10⁹⁡(96-digit number)
59806110442118473490…30478162545978849281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.196 Γ— 10⁹⁢(97-digit number)
11961222088423694698…60956325091957698561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.392 Γ— 10⁹⁢(97-digit number)
23922444176847389396…21912650183915397121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.784 Γ— 10⁹⁢(97-digit number)
47844888353694778792…43825300367830794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.568 Γ— 10⁹⁢(97-digit number)
95689776707389557585…87650600735661588481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.913 Γ— 10⁹⁷(98-digit number)
19137955341477911517…75301201471323176961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.827 Γ— 10⁹⁷(98-digit number)
38275910682955823034…50602402942646353921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.655 Γ— 10⁹⁷(98-digit number)
76551821365911646068…01204805885292707841
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:β€”
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