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Block #1,740,558

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/30/2016, 9:03:23 AM Β· Difficulty 10.7204 Β· 5,104,232 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d7898145c07d9429c0addbf0a177ce9557baec349faa8d5b229d3e5215072983
View on Chainz β†—

Height

#1,740,558

Difficulty

10.720351

Transactions

1

Size

242 B

Version

2

Bits

0ab868ea

Nonce

533,486,873

Timestamp

8/30/2016, 9:03:23 AM

Confirmations

5,104,232

Mined by

⛏️ P2SHAGkY5Euz5mzpuyGoaReCtspzag5TxsxHeG

Merkle Root

48742ce421cee6a48958169efb1db161c7ce0b429beefc8feb025461c81e4acd
Transactions (1)
Coinbase48742ce421cee6…025461c81e4acd
1 in β†’ 2 out8.6900 XPM152 B
AGkY5Euz…5TxsxHeGALPu3s2c…EJXLjVFh
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.

1.084 Γ— 10⁹⁡(96-digit number)
10848160023581111193…03621642503298336121
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
1.084 Γ— 10⁹⁡(96-digit number)
10848160023581111193…03621642503298336121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.169 Γ— 10⁹⁡(96-digit number)
21696320047162222386…07243285006596672241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.339 Γ— 10⁹⁡(96-digit number)
43392640094324444772…14486570013193344481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.678 Γ— 10⁹⁡(96-digit number)
86785280188648889544…28973140026386688961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.735 Γ— 10⁹⁢(97-digit number)
17357056037729777908…57946280052773377921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.471 Γ— 10⁹⁢(97-digit number)
34714112075459555817…15892560105546755841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.942 Γ— 10⁹⁢(97-digit number)
69428224150919111635…31785120211093511681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.388 Γ— 10⁹⁷(98-digit number)
13885644830183822327…63570240422187023361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.777 Γ— 10⁹⁷(98-digit number)
27771289660367644654…27140480844374046721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.554 Γ— 10⁹⁷(98-digit number)
55542579320735289308…54280961688748093441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:58,002,733 XPMΒ·at block #6,844,789 Β· updates every 60s
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