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Block #2,833,412

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 5:31:28 PM Β· Difficulty 11.7159 Β· 4,007,104 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51c6521a87dacc7f51bec4012be107e43e55b8e989e54914958f8a753c73ce07
View on Chainz β†—

Height

#2,833,412

Difficulty

11.715940

Transactions

1

Size

200 B

Version

2

Bits

0bb747d9

Nonce

1,388,631,791

Timestamp

9/10/2018, 5:31:28 PM

Confirmations

4,007,104

Mined by

⛏️ P2SHAZNDshfFPUoKiynqRXEPkyoL1VqAbc9VC1

Merkle Root

8d65504bdf3340b24125a997e4c2f82ed3817ab1e6ade6fd6ca1a969da59fb2a
Transactions (1)
Coinbase8d65504bdf3340…a1a969da59fb2a
1 in β†’ 1 out7.2700 XPM110 B
AZNDshfF…qAbc9VC1
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.

6.821 Γ— 10⁹⁴(95-digit number)
68219772641198053128…12568820393076981441
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
6.821 Γ— 10⁹⁴(95-digit number)
68219772641198053128…12568820393076981441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.364 Γ— 10⁹⁡(96-digit number)
13643954528239610625…25137640786153962881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.728 Γ— 10⁹⁡(96-digit number)
27287909056479221251…50275281572307925761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.457 Γ— 10⁹⁡(96-digit number)
54575818112958442502…00550563144615851521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.091 Γ— 10⁹⁢(97-digit number)
10915163622591688500…01101126289231703041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.183 Γ— 10⁹⁢(97-digit number)
21830327245183377001…02202252578463406081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.366 Γ— 10⁹⁢(97-digit number)
43660654490366754002…04404505156926812161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.732 Γ— 10⁹⁢(97-digit number)
87321308980733508004…08809010313853624321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.746 Γ— 10⁹⁷(98-digit number)
17464261796146701600…17618020627707248641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.492 Γ— 10⁹⁷(98-digit number)
34928523592293403201…35236041255414497281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.985 Γ— 10⁹⁷(98-digit number)
69857047184586806403…70472082510828994561
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:57,968,456 XPMΒ·at block #6,840,515 Β· updates every 60s
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