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Block #445,111

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/15/2014, 4:26:36 PM Β· Difficulty 10.3546 Β· 6,365,565 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
171e6ef5dc93a94a8dcf23286d239e87bb94638a1615fbc07ac87caea6a981b8
View on Chainz β†—

Height

#445,111

Difficulty

10.354596

Transactions

2

Size

393 B

Version

2

Bits

0a5ac6d1

Nonce

89,580

Timestamp

3/15/2014, 4:26:36 PM

Confirmations

6,365,565

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0b94912c0cb928e3446aaaff99ef1fff2b4faf1498df019a4a9f2cfa62703731
Transactions (2)
Coinbase1f44cfab094fb5…c3438efab42718
1 in β†’ 1 out9.3215 XPM110 B
AeKNrjNj…1NEq95Ta
ab8d0cf9b34902…ccf26a006e4175
1 in β†’ 1 out0.9900 XPM192 B
ARxpQYdD…q9Bde3dv
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.

1.513 Γ— 10⁹⁷(98-digit number)
15135736471529614379…55577456172650387399
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
1.513 Γ— 10⁹⁷(98-digit number)
15135736471529614379…55577456172650387399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.027 Γ— 10⁹⁷(98-digit number)
30271472943059228758…11154912345300774799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.054 Γ— 10⁹⁷(98-digit number)
60542945886118457517…22309824690601549599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.210 Γ— 10⁹⁸(99-digit number)
12108589177223691503…44619649381203099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.421 Γ— 10⁹⁸(99-digit number)
24217178354447383007…89239298762406198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.843 Γ— 10⁹⁸(99-digit number)
48434356708894766014…78478597524812396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.686 Γ— 10⁹⁸(99-digit number)
96868713417789532028…56957195049624793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.937 Γ— 10⁹⁹(100-digit number)
19373742683557906405…13914390099249587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.874 Γ— 10⁹⁹(100-digit number)
38747485367115812811…27828780198499174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.749 Γ— 10⁹⁹(100-digit number)
77494970734231625622…55657560396998348799
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:57,729,500 XPMΒ·at block #6,810,675 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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