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Block #111,841

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/11/2013, 4:10:22 PM Β· Difficulty 9.7140 Β· 6,683,324 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e51e81acf1352893d6b54b075d1afcad33b41b620c4b6dc98fd7cb1a5f83811d
View on Chainz β†—

Height

#111,841

Difficulty

9.714004

Transactions

2

Size

358 B

Version

2

Bits

09b6c8f8

Nonce

224,827

Timestamp

8/11/2013, 4:10:22 PM

Confirmations

6,683,324

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

ba5214f6a8c8b910c4137e1f6535d6b6d70409484b427bc023173ea9beecc5e9
Transactions (2)
Coinbase24e4aea563f19e…23250e49e35d2a
1 in β†’ 1 out10.5900 XPM109 B
AYyPPXgF…b6nr5cD2
4b5da4c4272475…77061727e7efa7
1 in β†’ 1 out10.9400 XPM158 B
AVtj9fEt…5iKvQNA1
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.

3.642 Γ— 10⁹⁷(98-digit number)
36427296379691095639…06042901259433855581
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
3.642 Γ— 10⁹⁷(98-digit number)
36427296379691095639…06042901259433855581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.285 Γ— 10⁹⁷(98-digit number)
72854592759382191278…12085802518867711161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.457 Γ— 10⁹⁸(99-digit number)
14570918551876438255…24171605037735422321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.914 Γ— 10⁹⁸(99-digit number)
29141837103752876511…48343210075470844641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.828 Γ— 10⁹⁸(99-digit number)
58283674207505753022…96686420150941689281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.165 Γ— 10⁹⁹(100-digit number)
11656734841501150604…93372840301883378561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.331 Γ— 10⁹⁹(100-digit number)
23313469683002301209…86745680603766757121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.662 Γ— 10⁹⁹(100-digit number)
46626939366004602418…73491361207533514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.325 Γ— 10⁹⁹(100-digit number)
93253878732009204836…46982722415067028481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,605,365 XPMΒ·at block #6,795,164 Β· updates every 60s
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