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Block #2,836,575

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2018, 10:15:46 PM Β· Difficulty 11.7160 Β· 4,006,578 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e74b28e8ba70ecb33cf6b97c1e112bcc4b6a954b2678935b27c3ee4626c0ed9
View on Chainz β†—

Height

#2,836,575

Difficulty

11.716015

Transactions

1

Size

201 B

Version

2

Bits

0bb74cc5

Nonce

127,565,507

Timestamp

9/12/2018, 10:15:46 PM

Confirmations

4,006,578

Mined by

⛏️ P2SHAXix5nKMQ9YujGcv4PCUSHkj5KpgGXvpmG

Merkle Root

2d8d9b86d01522c4ae534a8b407b69b589e3bf1370b6430252b02c332529cad1
Transactions (1)
Coinbase2d8d9b86d01522…b02c332529cad1
1 in β†’ 1 out7.2700 XPM110 B
AXix5nKM…pgGXvpmG
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.

1.678 Γ— 10⁹⁸(99-digit number)
16781845843654144195…27126626861947944961
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
1.678 Γ— 10⁹⁸(99-digit number)
16781845843654144195…27126626861947944961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.356 Γ— 10⁹⁸(99-digit number)
33563691687308288390…54253253723895889921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.712 Γ— 10⁹⁸(99-digit number)
67127383374616576780…08506507447791779841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.342 Γ— 10⁹⁹(100-digit number)
13425476674923315356…17013014895583559681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.685 Γ— 10⁹⁹(100-digit number)
26850953349846630712…34026029791167119361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.370 Γ— 10⁹⁹(100-digit number)
53701906699693261424…68052059582334238721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.074 Γ— 10¹⁰⁰(101-digit number)
10740381339938652284…36104119164668477441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.148 Γ— 10¹⁰⁰(101-digit number)
21480762679877304569…72208238329336954881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.296 Γ— 10¹⁰⁰(101-digit number)
42961525359754609139…44416476658673909761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.592 Γ— 10¹⁰⁰(101-digit number)
85923050719509218279…88832953317347819521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.718 Γ— 10¹⁰¹(102-digit number)
17184610143901843655…77665906634695639041
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:57,989,590 XPMΒ·at block #6,843,152 Β· updates every 60s
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