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Block #344,704

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/5/2014, 11:20:48 AM Β· Difficulty 10.2007 Β· 6,451,708 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
929e4dbf55971b279c5f98d6525fbb8ff3cd6ff787e453f7bdd33587067ba24f
View on Chainz β†—

Height

#344,704

Difficulty

10.200705

Transactions

1

Size

200 B

Version

2

Bits

0a336163

Nonce

583,007

Timestamp

1/5/2014, 11:20:48 AM

Confirmations

6,451,708

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b3369b8100ae31fb1c14d40c19aa5fb899433697de1d5a7f425a84ad5a498821
Transactions (1)
Coinbaseb3369b8100ae31…5a84ad5a498821
1 in β†’ 1 out9.6000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.755 Γ— 10⁹³(94-digit number)
37550255832815975134…60858738043391569281
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
3.755 Γ— 10⁹³(94-digit number)
37550255832815975134…60858738043391569281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.510 Γ— 10⁹³(94-digit number)
75100511665631950268…21717476086783138561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.502 Γ— 10⁹⁴(95-digit number)
15020102333126390053…43434952173566277121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.004 Γ— 10⁹⁴(95-digit number)
30040204666252780107…86869904347132554241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.008 Γ— 10⁹⁴(95-digit number)
60080409332505560214…73739808694265108481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.201 Γ— 10⁹⁡(96-digit number)
12016081866501112042…47479617388530216961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.403 Γ— 10⁹⁡(96-digit number)
24032163733002224085…94959234777060433921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.806 Γ— 10⁹⁡(96-digit number)
48064327466004448171…89918469554120867841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.612 Γ— 10⁹⁡(96-digit number)
96128654932008896343…79836939108241735681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.922 Γ— 10⁹⁢(97-digit number)
19225730986401779268…59673878216483471361
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:57,615,284 XPMΒ·at block #6,796,411 Β· updates every 60s
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