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Block #48,263

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 2:33:31 PM Β· Difficulty 8.8408 Β· 6,754,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
41d617e10568a6e1d6413000c596ea93615415a327e1f149cd5b2bd9a87bb592
View on Chainz β†—

Height

#48,263

Difficulty

8.840821

Transactions

1

Size

200 B

Version

2

Bits

08d74005

Nonce

348

Timestamp

7/15/2013, 2:33:31 PM

Confirmations

6,754,410

Mined by

⛏️ P2SHAaZ1y25a3SDUcqzGJtgt1hGaUYEJhHnPEm

Merkle Root

da4fae2e747fc61ac96fe33a869876b8f4f2be68d50e468cc4f75722cd83b547
Transactions (1)
Coinbaseda4fae2e747fc6…f75722cd83b547
1 in β†’ 1 out12.7800 XPM110 B
AaZ1y25a…EJhHnPEm
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.

1.078 Γ— 10⁹⁡(96-digit number)
10784150616607356147…61623109406417029401
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
1.078 Γ— 10⁹⁡(96-digit number)
10784150616607356147…61623109406417029401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.156 Γ— 10⁹⁡(96-digit number)
21568301233214712295…23246218812834058801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.313 Γ— 10⁹⁡(96-digit number)
43136602466429424591…46492437625668117601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.627 Γ— 10⁹⁡(96-digit number)
86273204932858849183…92984875251336235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.725 Γ— 10⁹⁢(97-digit number)
17254640986571769836…85969750502672470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.450 Γ— 10⁹⁢(97-digit number)
34509281973143539673…71939501005344940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.901 Γ— 10⁹⁢(97-digit number)
69018563946287079347…43879002010689881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.380 Γ— 10⁹⁷(98-digit number)
13803712789257415869…87758004021379763201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,665,404 XPMΒ·at block #6,802,672 Β· updates every 60s
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