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Block #295,311

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 9:12:03 AM Β· Difficulty 9.9913 Β· 6,517,525 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c6b4e1fdd2e0c7d39e8c7ff8a7cf65c2fe2da902af68ce3ac7d2ee6ed71ee9a5
View on Chainz β†—

Height

#295,311

Difficulty

9.991324

Transactions

1

Size

198 B

Version

2

Bits

09fdc767

Nonce

13,703

Timestamp

12/5/2013, 9:12:03 AM

Confirmations

6,517,525

Mined by

⛏️ P2SHAbWzNQQfdk7tsLEZbLbmi1xqR4bAY9RJig

Merkle Root

1e2a386b322fdce5221919bbcb0f784b04794b9bee5bef6ccc20afa5692239ca
Transactions (1)
Coinbase1e2a386b322fdc…20afa5692239ca
1 in β†’ 1 out10.0000 XPM109 B
AbWzNQQf…bAY9RJig
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.

2.243 Γ— 10⁹²(93-digit number)
22437547865337369318…44053993498501080159
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
2.243 Γ— 10⁹²(93-digit number)
22437547865337369318…44053993498501080159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.487 Γ— 10⁹²(93-digit number)
44875095730674738637…88107986997002160319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.975 Γ— 10⁹²(93-digit number)
89750191461349477274…76215973994004320639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.795 Γ— 10⁹³(94-digit number)
17950038292269895454…52431947988008641279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.590 Γ— 10⁹³(94-digit number)
35900076584539790909…04863895976017282559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.180 Γ— 10⁹³(94-digit number)
71800153169079581819…09727791952034565119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁴(95-digit number)
14360030633815916363…19455583904069130239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁴(95-digit number)
28720061267631832727…38911167808138260479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.744 Γ— 10⁹⁴(95-digit number)
57440122535263665455…77822335616276520959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁡(96-digit number)
11488024507052733091…55644671232553041919
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:57,746,733 XPMΒ·at block #6,812,835 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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