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Block #2,833,156

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 1:35:28 PM Β· Difficulty 11.7148 Β· 4,007,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0e1a2271bdea7a43a6bd48a7b1816e2ca58233c1ef76378482b20f794de3857
View on Chainz β†—

Height

#2,833,156

Difficulty

11.714790

Transactions

1

Size

201 B

Version

2

Bits

0bb6fc7c

Nonce

238,443,074

Timestamp

9/10/2018, 1:35:28 PM

Confirmations

4,007,656

Mined by

⛏️ P2SHAN4FyT9cKbEj1irGeA8G2VS1mz8bBdwZ5x

Merkle Root

056d4b057b7e7c06a42e87b04390ea402043a06e713f9929a134c7254d9bd965
Transactions (1)
Coinbase056d4b057b7e7c…34c7254d9bd965
1 in β†’ 1 out7.2700 XPM110 B
AN4FyT9c…8bBdwZ5x
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.

6.343 Γ— 10⁹⁢(97-digit number)
63431767800911559835…41518206443414609921
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
6.343 Γ— 10⁹⁢(97-digit number)
63431767800911559835…41518206443414609921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.268 Γ— 10⁹⁷(98-digit number)
12686353560182311967…83036412886829219841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.537 Γ— 10⁹⁷(98-digit number)
25372707120364623934…66072825773658439681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.074 Γ— 10⁹⁷(98-digit number)
50745414240729247868…32145651547316879361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.014 Γ— 10⁹⁸(99-digit number)
10149082848145849573…64291303094633758721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.029 Γ— 10⁹⁸(99-digit number)
20298165696291699147…28582606189267517441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.059 Γ— 10⁹⁸(99-digit number)
40596331392583398294…57165212378535034881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.119 Γ— 10⁹⁸(99-digit number)
81192662785166796589…14330424757070069761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.623 Γ— 10⁹⁹(100-digit number)
16238532557033359317…28660849514140139521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.247 Γ— 10⁹⁹(100-digit number)
32477065114066718635…57321699028280279041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.495 Γ— 10⁹⁹(100-digit number)
64954130228133437271…14643398056560558081
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:57,970,847 XPMΒ·at block #6,840,811 Β· updates every 60s
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