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Block #344,831

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/5/2014, 1:23:52 PM Β· Difficulty 10.2011 Β· 6,469,404 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a45c91da7773b1cb485cfc73b98b141359e30f361ab5af94738ac6f973a71784
View on Chainz β†—

Height

#344,831

Difficulty

10.201063

Transactions

2

Size

537 B

Version

2

Bits

0a3378d6

Nonce

37,443

Timestamp

1/5/2014, 1:23:52 PM

Confirmations

6,469,404

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

633e92929e0963b88e33ec447146215ce5d0d0aeee39bd1b9a8c921ef03693ac
Transactions (2)
Coinbasefe5d3299ca6275…3065cc7d8491c9
1 in β†’ 1 out9.6100 XPM110 B
AeKNrjNj…1NEq95Ta
bf5498cfc49ce9…90db3c4e8b1dca
2 in β†’ 1 out4.7921 XPM338 B
AVUKrrMP…xy3Qxujc
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.

3.133 Γ— 10⁹²(93-digit number)
31337383702154745176…40698012703245359441
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
3.133 Γ— 10⁹²(93-digit number)
31337383702154745176…40698012703245359441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.267 Γ— 10⁹²(93-digit number)
62674767404309490353…81396025406490718881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.253 Γ— 10⁹³(94-digit number)
12534953480861898070…62792050812981437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.506 Γ— 10⁹³(94-digit number)
25069906961723796141…25584101625962875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.013 Γ— 10⁹³(94-digit number)
50139813923447592283…51168203251925751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.002 Γ— 10⁹⁴(95-digit number)
10027962784689518456…02336406503851502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.005 Γ— 10⁹⁴(95-digit number)
20055925569379036913…04672813007703004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.011 Γ— 10⁹⁴(95-digit number)
40111851138758073826…09345626015406008321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.022 Γ— 10⁹⁴(95-digit number)
80223702277516147653…18691252030812016641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.604 Γ— 10⁹⁡(96-digit number)
16044740455503229530…37382504061624033281
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:57,757,952 XPMΒ·at block #6,814,234 Β· updates every 60s
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