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Block #342,748

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2014, 6:35:15 AM Β· Difficulty 10.1626 Β· 6,473,696 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1645505f477fcff7b6f9e656bcaf09f4003cb2147bf7239fc6b96b9b700d6437
View on Chainz β†—

Height

#342,748

Difficulty

10.162603

Transactions

1

Size

206 B

Version

2

Bits

0a29a062

Nonce

61,530

Timestamp

1/4/2014, 6:35:15 AM

Confirmations

6,473,696

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e5ebc47b60725359ab3ebf9b3b003187d475fd0c88f44e94e0d3046a5bd46583
Transactions (1)
Coinbasee5ebc47b607253…d3046a5bd46583
1 in β†’ 1 out9.6700 XPM116 B
AbwWkWZt…kawDhufa
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.

1.841 Γ— 10⁹⁴(95-digit number)
18413975023115025501…87150447145391198719
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.841 Γ— 10⁹⁴(95-digit number)
18413975023115025501…87150447145391198719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.682 Γ— 10⁹⁴(95-digit number)
36827950046230051002…74300894290782397439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.365 Γ— 10⁹⁴(95-digit number)
73655900092460102004…48601788581564794879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.473 Γ— 10⁹⁡(96-digit number)
14731180018492020400…97203577163129589759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.946 Γ— 10⁹⁡(96-digit number)
29462360036984040801…94407154326259179519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.892 Γ— 10⁹⁡(96-digit number)
58924720073968081603…88814308652518359039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.178 Γ— 10⁹⁢(97-digit number)
11784944014793616320…77628617305036718079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.356 Γ— 10⁹⁢(97-digit number)
23569888029587232641…55257234610073436159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.713 Γ— 10⁹⁢(97-digit number)
47139776059174465282…10514469220146872319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.427 Γ— 10⁹⁢(97-digit number)
94279552118348930565…21028938440293744639
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,775,678 XPMΒ·at block #6,816,443 Β· updates every 60s
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