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Block #55,118

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 12:03:29 AM Β· Difficulty 8.9393 Β· 6,753,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
53ff2f04de89cc4aaaafacc060edc849ff5fa90495e86509ca1afef2d2b12f01
View on Chainz β†—

Height

#55,118

Difficulty

8.939264

Transactions

2

Size

356 B

Version

2

Bits

08f07397

Nonce

12

Timestamp

7/17/2013, 12:03:29 AM

Confirmations

6,753,311

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

94b0cfa51d5733da09d0e4a02943e3ec40174c0d558b5988a750a380f09c5575
Transactions (2)
Coinbase1ecb7849afd47f…cd8028918e3188
1 in β†’ 1 out12.5100 XPM110 B
AXY6feyt…oghmWWGf
c633d3ec152262…7bfbc2c53cce3b
1 in β†’ 1 out12.6100 XPM159 B
AWZPS4WA…7LQazeJT
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.

2.101 Γ— 10⁸⁷(88-digit number)
21012493455134346712…66402602224745592491
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
2.101 Γ— 10⁸⁷(88-digit number)
21012493455134346712…66402602224745592491
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.202 Γ— 10⁸⁷(88-digit number)
42024986910268693425…32805204449491184981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.404 Γ— 10⁸⁷(88-digit number)
84049973820537386851…65610408898982369961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.680 Γ— 10⁸⁸(89-digit number)
16809994764107477370…31220817797964739921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.361 Γ— 10⁸⁸(89-digit number)
33619989528214954740…62441635595929479841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.723 Γ— 10⁸⁸(89-digit number)
67239979056429909481…24883271191858959681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.344 Γ— 10⁸⁹(90-digit number)
13447995811285981896…49766542383717919361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.689 Γ— 10⁸⁹(90-digit number)
26895991622571963792…99533084767435838721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.379 Γ— 10⁸⁹(90-digit number)
53791983245143927585…99066169534871677441
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:57,711,492 XPMΒ·at block #6,808,428 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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