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Block #113,305

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2013, 11:22:48 AM Β· Difficulty 9.7311 Β· 6,696,851 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
662251673dbc5545f58bd83fdc57f2871f1a4eb42a19d81f1b0e58e7e3c10785
View on Chainz β†—

Height

#113,305

Difficulty

9.731120

Transactions

1

Size

200 B

Version

2

Bits

09bb2ab0

Nonce

151,119

Timestamp

8/12/2013, 11:22:48 AM

Confirmations

6,696,851

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

87e85018aba9907d69a9eee4ed68a73b6103cc0dd1b928e0fad9f77aa088c8dd
Transactions (1)
Coinbase87e85018aba990…d9f77aa088c8dd
1 in β†’ 1 out10.5400 XPM109 B
AezMwyLP…rTg7Eyfk
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.

5.515 Γ— 10⁹⁢(97-digit number)
55152545343152909411…77478149120178165231
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
5.515 Γ— 10⁹⁢(97-digit number)
55152545343152909411…77478149120178165231
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.103 Γ— 10⁹⁷(98-digit number)
11030509068630581882…54956298240356330461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.206 Γ— 10⁹⁷(98-digit number)
22061018137261163764…09912596480712660921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.412 Γ— 10⁹⁷(98-digit number)
44122036274522327529…19825192961425321841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.824 Γ— 10⁹⁷(98-digit number)
88244072549044655058…39650385922850643681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.764 Γ— 10⁹⁸(99-digit number)
17648814509808931011…79300771845701287361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.529 Γ— 10⁹⁸(99-digit number)
35297629019617862023…58601543691402574721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.059 Γ— 10⁹⁸(99-digit number)
70595258039235724047…17203087382805149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.411 Γ— 10⁹⁹(100-digit number)
14119051607847144809…34406174765610298881
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:57,725,314 XPMΒ·at block #6,810,155 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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