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Block #2,131,295

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 12:19:33 AM Β· Difficulty 10.9101 Β· 4,711,310 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f2ef6b88299bbf1c7befc4bec1f113f5093a598b5e0fbc310055afb4df86d937
View on Chainz β†—

Height

#2,131,295

Difficulty

10.910126

Transactions

1

Size

200 B

Version

2

Bits

0ae8fe0a

Nonce

1,249,245,214

Timestamp

5/25/2017, 12:19:33 AM

Confirmations

4,711,310

Mined by

⛏️ P2SHAWWt88uW31jP5ox8bK7VC9Vr1nZZ4QqbU7

Merkle Root

2c474faf8b5fad01b88245755bfe4225ebecfcb4a19da09e74643d91ff66e985
Transactions (1)
Coinbase2c474faf8b5fad…643d91ff66e985
1 in β†’ 1 out8.3900 XPM109 B
AWWt88uW…ZZ4QqbU7
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.

1.041 Γ— 10⁹⁢(97-digit number)
10412204558866250077…99834672837812812801
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
1.041 Γ— 10⁹⁢(97-digit number)
10412204558866250077…99834672837812812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.082 Γ— 10⁹⁢(97-digit number)
20824409117732500154…99669345675625625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.164 Γ— 10⁹⁢(97-digit number)
41648818235465000309…99338691351251251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.329 Γ— 10⁹⁢(97-digit number)
83297636470930000619…98677382702502502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.665 Γ— 10⁹⁷(98-digit number)
16659527294186000123…97354765405005004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.331 Γ— 10⁹⁷(98-digit number)
33319054588372000247…94709530810010009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.663 Γ— 10⁹⁷(98-digit number)
66638109176744000495…89419061620020019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.332 Γ— 10⁹⁸(99-digit number)
13327621835348800099…78838123240040038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.665 Γ— 10⁹⁸(99-digit number)
26655243670697600198…57676246480080076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.331 Γ— 10⁹⁸(99-digit number)
53310487341395200396…15352492960160153601
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:57,985,269 XPMΒ·at block #6,842,604 Β· updates every 60s
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