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Block #346,262

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/6/2014, 10:57:58 AM Β· Difficulty 10.2219 Β· 6,459,614 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4bf8626aa9edf7354d00cf3575ac13619b5351a6bd42f8d8d21fa179c0a08cca
View on Chainz β†—

Height

#346,262

Difficulty

10.221905

Transactions

2

Size

574 B

Version

2

Bits

0a38cec1

Nonce

34,396

Timestamp

1/6/2014, 10:57:58 AM

Confirmations

6,459,614

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

225af25810b4f092ae1f033e9f3eb9a94398838b0ac256bbbdfe306c1ff0f5ee
Transactions (2)
Coinbase52873f6af41000…ae3633b588f259
1 in β†’ 1 out9.5700 XPM110 B
AeKNrjNj…1NEq95Ta
550aa708d9f185…a8831a9d1d8cc7
2 in β†’ 2 out2.0195 XPM374 B
AW2fxtLH…F53KgUi3AFpfQwU3…rChsvy6H
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.

4.889 Γ— 10⁹⁡(96-digit number)
48899839976436533823…95023083754488485001
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
4.889 Γ— 10⁹⁡(96-digit number)
48899839976436533823…95023083754488485001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.779 Γ— 10⁹⁡(96-digit number)
97799679952873067646…90046167508976970001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.955 Γ— 10⁹⁢(97-digit number)
19559935990574613529…80092335017953940001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.911 Γ— 10⁹⁢(97-digit number)
39119871981149227058…60184670035907880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.823 Γ— 10⁹⁢(97-digit number)
78239743962298454117…20369340071815760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.564 Γ— 10⁹⁷(98-digit number)
15647948792459690823…40738680143631520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.129 Γ— 10⁹⁷(98-digit number)
31295897584919381646…81477360287263040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.259 Γ— 10⁹⁷(98-digit number)
62591795169838763293…62954720574526080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.251 Γ— 10⁹⁸(99-digit number)
12518359033967752658…25909441149052160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.503 Γ— 10⁹⁸(99-digit number)
25036718067935505317…51818882298104320001
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:57,691,092 XPMΒ·at block #6,805,875 Β· updates every 60s
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