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Block #104,981

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 7:35:30 AM Β· Difficulty 9.5719 Β· 6,720,482 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5dd8bc2a8823b2a0b3ee94e07407265f98d5ac081742c8c467c8ec922f1f5e02
View on Chainz β†—

Height

#104,981

Difficulty

9.571867

Transactions

1

Size

201 B

Version

2

Bits

099265d9

Nonce

2,167

Timestamp

8/8/2013, 7:35:30 AM

Confirmations

6,720,482

Mined by

⛏️ P2SHAQPnMu4biuyvLRic2sEMTAeoRp4cQt9Z4q

Merkle Root

4fd9928653cde57f76181ef5da51d929d075d043c27b8cd1aa609e62f0683e2f
Transactions (1)
Coinbase4fd9928653cde5…609e62f0683e2f
1 in β†’ 1 out10.9000 XPM109 B
AQPnMu4b…4cQt9Z4q
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.

8.076 Γ— 10⁹⁹(100-digit number)
80761182931337277876…41492578730997845329
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
8.076 Γ— 10⁹⁹(100-digit number)
80761182931337277876…41492578730997845329
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.615 Γ— 10¹⁰⁰(101-digit number)
16152236586267455575…82985157461995690659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.230 Γ— 10¹⁰⁰(101-digit number)
32304473172534911150…65970314923991381319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.460 Γ— 10¹⁰⁰(101-digit number)
64608946345069822300…31940629847982762639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.292 Γ— 10¹⁰¹(102-digit number)
12921789269013964460…63881259695965525279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.584 Γ— 10¹⁰¹(102-digit number)
25843578538027928920…27762519391931050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.168 Γ— 10¹⁰¹(102-digit number)
51687157076055857840…55525038783862101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.033 Γ— 10¹⁰²(103-digit number)
10337431415211171568…11050077567724202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.067 Γ— 10¹⁰²(103-digit number)
20674862830422343136…22100155135448404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.134 Γ— 10¹⁰²(103-digit number)
41349725660844686272…44200310270896808959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,847,807 XPMΒ·at block #6,825,462 Β· updates every 60s
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