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Block #103,205

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 11:48:59 AM Β· Difficulty 9.5189 Β· 6,694,947 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a3d0a8f7f2805e10da92a1604c1536150b99bd426de13fc1e4b4f33956bdc32f
View on Chainz β†—

Height

#103,205

Difficulty

9.518940

Transactions

3

Size

1.76 KB

Version

2

Bits

0984d944

Nonce

232,637

Timestamp

8/7/2013, 11:48:59 AM

Confirmations

6,694,947

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

6c0c0af44d11d6b8d93fa2cb16502042694dff61ffcb57ca1f4c094e9c11d75e
Transactions (3)
Coinbasee544067a31fd02…c96d55638bc0e7
1 in β†’ 1 out11.0500 XPM109 B
AYyPPXgF…b6nr5cD2
1deb157a72a4f6…891af3bdaf8cba
12 in β†’ 1 out200.0000 XPM1.38 KB
AYAQu6v9…Huu7nZAE
0b45d93b05be9b…323ab410e460bb
1 in β†’ 2 out11.2800 XPM193 B
AYQgZje2…fn4pgV5RARsNkN3a…BVC8Lvw4
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.

8.347 Γ— 10⁹⁴(95-digit number)
83478066350449471547…95080517524981520001
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
8.347 Γ— 10⁹⁴(95-digit number)
83478066350449471547…95080517524981520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.669 Γ— 10⁹⁡(96-digit number)
16695613270089894309…90161035049963040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.339 Γ— 10⁹⁡(96-digit number)
33391226540179788619…80322070099926080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.678 Γ— 10⁹⁡(96-digit number)
66782453080359577238…60644140199852160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.335 Γ— 10⁹⁢(97-digit number)
13356490616071915447…21288280399704320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.671 Γ— 10⁹⁢(97-digit number)
26712981232143830895…42576560799408640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.342 Γ— 10⁹⁢(97-digit number)
53425962464287661790…85153121598817280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.068 Γ— 10⁹⁷(98-digit number)
10685192492857532358…70306243197634560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.137 Γ— 10⁹⁷(98-digit number)
21370384985715064716…40612486395269120001
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:57,629,215 XPMΒ·at block #6,798,151 Β· updates every 60s
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