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Block #239,691

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/2/2013, 6:17:57 AM Β· Difficulty 9.9546 Β· 6,571,041 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
07d160d8d4f8a206890d9f3fce7754b6f423a54b21aafcd597fd38f0ce99dcf0
View on Chainz β†—

Height

#239,691

Difficulty

9.954608

Transactions

1

Size

199 B

Version

2

Bits

09f46135

Nonce

64,273

Timestamp

11/2/2013, 6:17:57 AM

Confirmations

6,571,041

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

f9fa4dfdd0366e47361c57935c091a974019b20dfbd861cfd04a7841679793b3
Transactions (1)
Coinbasef9fa4dfdd0366e…4a7841679793b3
1 in β†’ 1 out10.0800 XPM109 B
AFv4Gxfh…LfEWFx48
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.

1.823 Γ— 10⁹⁡(96-digit number)
18234345042316240992…77091866617240138751
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
1.823 Γ— 10⁹⁡(96-digit number)
18234345042316240992…77091866617240138751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.646 Γ— 10⁹⁡(96-digit number)
36468690084632481984…54183733234480277501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.293 Γ— 10⁹⁡(96-digit number)
72937380169264963968…08367466468960555001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.458 Γ— 10⁹⁢(97-digit number)
14587476033852992793…16734932937921110001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.917 Γ— 10⁹⁢(97-digit number)
29174952067705985587…33469865875842220001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.834 Γ— 10⁹⁢(97-digit number)
58349904135411971174…66939731751684440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.166 Γ— 10⁹⁷(98-digit number)
11669980827082394234…33879463503368880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.333 Γ— 10⁹⁷(98-digit number)
23339961654164788469…67758927006737760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.667 Γ— 10⁹⁷(98-digit number)
46679923308329576939…35517854013475520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.335 Γ— 10⁹⁷(98-digit number)
93359846616659153879…71035708026951040001
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:57,729,946 XPMΒ·at block #6,810,731 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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