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Block #68,797

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 5:47:33 AM Β· Difficulty 8.9900 Β· 6,740,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8aee2d9f5e742e890769e5fb809b3d79908ca96009904ba65265212ed5ba52c1
View on Chainz β†—

Height

#68,797

Difficulty

8.990039

Transactions

1

Size

202 B

Version

2

Bits

08fd7333

Nonce

201

Timestamp

7/20/2013, 5:47:33 AM

Confirmations

6,740,935

Mined by

⛏️ P2SHANYe8KyPCpPzPnuRkCeGwL6TTHt58nkW75

Merkle Root

45563f3fa95e8d3c9d68946c162fdd8bceeea858b1c4ddb2c479571ea9ece14b
Transactions (1)
Coinbase45563f3fa95e8d…79571ea9ece14b
1 in β†’ 1 out12.3600 XPM110 B
ANYe8KyP…t58nkW75
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.

4.975 Γ— 10⁹⁹(100-digit number)
49752441117357122435…67227445664894041071
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
4.975 Γ— 10⁹⁹(100-digit number)
49752441117357122435…67227445664894041071
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.950 Γ— 10⁹⁹(100-digit number)
99504882234714244871…34454891329788082141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.990 Γ— 10¹⁰⁰(101-digit number)
19900976446942848974…68909782659576164281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.980 Γ— 10¹⁰⁰(101-digit number)
39801952893885697948…37819565319152328561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.960 Γ— 10¹⁰⁰(101-digit number)
79603905787771395897…75639130638304657121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.592 Γ— 10¹⁰¹(102-digit number)
15920781157554279179…51278261276609314241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.184 Γ— 10¹⁰¹(102-digit number)
31841562315108558359…02556522553218628481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.368 Γ— 10¹⁰¹(102-digit number)
63683124630217116718…05113045106437256961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.273 Γ— 10¹⁰²(103-digit number)
12736624926043423343…10226090212874513921
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:57,721,938 XPMΒ·at block #6,809,731 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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