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Block #289,048

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/2/2013, 12:51:49 AM Β· Difficulty 9.9882 Β· 6,521,209 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc407f92d37dd229e93a14305771626c12f3397d6fb59225572632788eae9373
View on Chainz β†—

Height

#289,048

Difficulty

9.988205

Transactions

1

Size

198 B

Version

2

Bits

09fcfafb

Nonce

45,219

Timestamp

12/2/2013, 12:51:49 AM

Confirmations

6,521,209

Mined by

⛏️ P2SHAVN5TcQu993EfviCkpQSYHiBxtuDJ9ZxKG

Merkle Root

1c1db67b1d2d03b71ba4791aad0108ec2fdc242866b0b579b81ba608a7892cd2
Transactions (1)
Coinbase1c1db67b1d2d03…1ba608a7892cd2
1 in β†’ 1 out10.0100 XPM109 B
AVN5TcQu…uDJ9ZxKG
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.

7.251 Γ— 10⁹¹(92-digit number)
72511065451086019887…19150646660691214399
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
7.251 Γ— 10⁹¹(92-digit number)
72511065451086019887…19150646660691214399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.450 Γ— 10⁹²(93-digit number)
14502213090217203977…38301293321382428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.900 Γ— 10⁹²(93-digit number)
29004426180434407955…76602586642764857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.800 Γ— 10⁹²(93-digit number)
58008852360868815910…53205173285529715199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.160 Γ— 10⁹³(94-digit number)
11601770472173763182…06410346571059430399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.320 Γ— 10⁹³(94-digit number)
23203540944347526364…12820693142118860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.640 Γ— 10⁹³(94-digit number)
46407081888695052728…25641386284237721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.281 Γ— 10⁹³(94-digit number)
92814163777390105456…51282772568475443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁴(95-digit number)
18562832755478021091…02565545136950886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.712 Γ— 10⁹⁴(95-digit number)
37125665510956042182…05131090273901772799
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:57,726,129 XPMΒ·at block #6,810,256 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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