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Block #48,761

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2013, 4:55:28 PM Β· Difficulty 8.8517 Β· 6,746,793 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e9541b855801edcad3836af39ca96506d5b19af07e091b7bb5299f2d401f7a71
View on Chainz β†—

Height

#48,761

Difficulty

8.851692

Transactions

3

Size

1.20 KB

Version

2

Bits

08da087f

Nonce

153

Timestamp

7/15/2013, 4:55:28 PM

Confirmations

6,746,793

Mined by

⛏️ P2SHAMyWD9ctQnmTLCp8dtHJVDeJpr53hiokZV

Merkle Root

add60febf409705ecead3f0ffe901a1e0bd1f2edb5d5fefa7688987830456131
Transactions (3)
Coinbase065e592b61de0f…f5e7afc99ac539
1 in β†’ 1 out12.7700 XPM110 B
AMyWD9ct…53hiokZV
0081b998a96569…e4c4b43e605ba7
6 in β†’ 1 out96.2400 XPM764 B
ATcXDU7J…Tn2sLLuN
3f24ee369f5ded…4efc564d1ecda6
2 in β†’ 1 out26.2600 XPM271 B
AG43TCYA…UW1AUz7e
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.

9.360 Γ— 10⁸⁸(89-digit number)
93609029930380212431…27992440363798080039
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.360 Γ— 10⁸⁸(89-digit number)
93609029930380212431…27992440363798080039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.872 Γ— 10⁸⁹(90-digit number)
18721805986076042486…55984880727596160079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.744 Γ— 10⁸⁹(90-digit number)
37443611972152084972…11969761455192320159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.488 Γ— 10⁸⁹(90-digit number)
74887223944304169945…23939522910384640319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.497 Γ— 10⁹⁰(91-digit number)
14977444788860833989…47879045820769280639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.995 Γ— 10⁹⁰(91-digit number)
29954889577721667978…95758091641538561279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.990 Γ— 10⁹⁰(91-digit number)
59909779155443335956…91516183283077122559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.198 Γ— 10⁹¹(92-digit number)
11981955831088667191…83032366566154245119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,608,497 XPMΒ·at block #6,795,553 Β· updates every 60s
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