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Block #105,516

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 1:43:08 PM Β· Difficulty 9.5860 Β· 6,704,048 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d75825a59b6d51a3055120ed7640f33c620f5b9d91868e4955d1b4c8fe127e3f
View on Chainz β†—

Height

#105,516

Difficulty

9.585978

Transactions

2

Size

358 B

Version

2

Bits

099602a0

Nonce

44,979

Timestamp

8/8/2013, 1:43:08 PM

Confirmations

6,704,048

Mined by

⛏️ P2SHAVU9RqZnigVh9QJToVYnazFrMZrhpQ1hgr

Merkle Root

e2ecebf3b0129a6a5a3ede3fa2b0f4facc1a57653766a8ba0dd9f663f73c06e2
Transactions (2)
Coinbase4b851265fbbfa8…97a75cca43dc40
1 in β†’ 1 out10.8800 XPM109 B
AVU9RqZn…rhpQ1hgr
659b1c72dff9aa…6b77a3c78509df
1 in β†’ 1 out11.0900 XPM157 B
ATareS7a…5FKKTQVH
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.

1.257 Γ— 10⁹⁹(100-digit number)
12575155004649403682…14786263706943111401
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
1.257 Γ— 10⁹⁹(100-digit number)
12575155004649403682…14786263706943111401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.515 Γ— 10⁹⁹(100-digit number)
25150310009298807364…29572527413886222801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.030 Γ— 10⁹⁹(100-digit number)
50300620018597614729…59145054827772445601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.006 Γ— 10¹⁰⁰(101-digit number)
10060124003719522945…18290109655544891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.012 Γ— 10¹⁰⁰(101-digit number)
20120248007439045891…36580219311089782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.024 Γ— 10¹⁰⁰(101-digit number)
40240496014878091783…73160438622179564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.048 Γ— 10¹⁰⁰(101-digit number)
80480992029756183567…46320877244359129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.609 Γ— 10¹⁰¹(102-digit number)
16096198405951236713…92641754488718259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.219 Γ— 10¹⁰¹(102-digit number)
32192396811902473427…85283508977436518401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,720,587 XPMΒ·at block #6,809,563 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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