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Block #105,746

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 4:29:21 PM Β· Difficulty 9.5911 Β· 6,699,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27507f03e45c0e9ee21a5ff985b6707fcbf03410b61e9eca54242662354fa9b9
View on Chainz β†—

Height

#105,746

Difficulty

9.591107

Transactions

1

Size

200 B

Version

2

Bits

099752c3

Nonce

65,720

Timestamp

8/8/2013, 4:29:21 PM

Confirmations

6,699,202

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

855d54e8177ce463a072f27375e38c2d1584043c0ad69a4f0bd9a8bd955f4ef4
Transactions (1)
Coinbase855d54e8177ce4…d9a8bd955f4ef4
1 in β†’ 1 out10.8500 XPM109 B
ASXW8s4r…LM8vqY9U
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.

6.904 Γ— 10⁹⁷(98-digit number)
69048251947200633417…40549066633693359881
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
6.904 Γ— 10⁹⁷(98-digit number)
69048251947200633417…40549066633693359881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.380 Γ— 10⁹⁸(99-digit number)
13809650389440126683…81098133267386719761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.761 Γ— 10⁹⁸(99-digit number)
27619300778880253367…62196266534773439521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.523 Γ— 10⁹⁸(99-digit number)
55238601557760506734…24392533069546879041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.104 Γ— 10⁹⁹(100-digit number)
11047720311552101346…48785066139093758081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.209 Γ— 10⁹⁹(100-digit number)
22095440623104202693…97570132278187516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.419 Γ— 10⁹⁹(100-digit number)
44190881246208405387…95140264556375032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.838 Γ— 10⁹⁹(100-digit number)
88381762492416810774…90280529112750064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.767 Γ— 10¹⁰⁰(101-digit number)
17676352498483362154…80561058225500129281
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:57,683,649 XPMΒ·at block #6,804,947 Β· updates every 60s
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