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Block #341,684

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/3/2014, 2:49:19 PM Β· Difficulty 10.1423 Β· 6,503,573 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a3718ec65c27641685ea1e78db5005af3f6e86f520f539734cb34e2c8dd8f211
View on Chainz β†—

Height

#341,684

Difficulty

10.142256

Transactions

2

Size

5.01 KB

Version

2

Bits

0a246add

Nonce

28,585

Timestamp

1/3/2014, 2:49:19 PM

Confirmations

6,503,573

Mined by

⛏️ P2SHAPV1gQNawtNVkLn1F9RbMB7VC64DY4WZab

Merkle Root

ec067e9ba7f7c01178c66ffea55f762addfdc698b1156399fd955b1ce3c08b94
Transactions (2)
Coinbasedf9ba99bbee231…680b1dd03d2cc0
1 in β†’ 1 out9.7600 XPM109 B
APV1gQNa…4DY4WZab
652461f93d82ea…e2bbb05fc3d5aa
33 in β†’ 1 out36.1150 XPM4.81 KB
AbB1VhGR…ZsRoj8Tw
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.

7.262 Γ— 10⁹⁡(96-digit number)
72627490410120072733…44234120293779347201
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
7.262 Γ— 10⁹⁡(96-digit number)
72627490410120072733…44234120293779347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.452 Γ— 10⁹⁢(97-digit number)
14525498082024014546…88468240587558694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.905 Γ— 10⁹⁢(97-digit number)
29050996164048029093…76936481175117388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.810 Γ— 10⁹⁢(97-digit number)
58101992328096058187…53872962350234777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.162 Γ— 10⁹⁷(98-digit number)
11620398465619211637…07745924700469555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.324 Γ— 10⁹⁷(98-digit number)
23240796931238423274…15491849400939110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.648 Γ— 10⁹⁷(98-digit number)
46481593862476846549…30983698801878220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.296 Γ— 10⁹⁷(98-digit number)
92963187724953693099…61967397603756441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.859 Γ— 10⁹⁸(99-digit number)
18592637544990738619…23934795207512883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.718 Γ— 10⁹⁸(99-digit number)
37185275089981477239…47869590415025766401
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:58,006,489 XPMΒ·at block #6,845,256 Β· updates every 60s
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