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Block #3,441,330

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/20/2019, 5:09:33 PM Β· Difficulty 10.9786 Β· 3,399,488 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3c1d85f63f9c5026ca5214db5624482c896c2580dc825d738b992fc3c2a0a83f
View on Chainz β†—

Height

#3,441,330

Difficulty

10.978647

Transactions

2

Size

2.40 KB

Version

2

Bits

0afa88a1

Nonce

1,166,098,975

Timestamp

11/20/2019, 5:09:33 PM

Confirmations

3,399,488

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

20c34a036fedd1a657b256e84db7dd220f3f9967b8b50dd49c71127f2cbdc048
Transactions (2)
Coinbase507429ebbbdc31…53b71a4b22a3fe
1 in β†’ 1 out8.3100 XPM109 B
ASiq2qtK…VMhmk7yL
3de1bb4cd2f659…d2f7d99c70dba8
15 in β†’ 1 out150.6148 XPM2.21 KB
AXoSyMCe…Z8KXiWkn
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.

4.262 Γ— 10⁹⁴(95-digit number)
42628826687569728794…18260336429635678129
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
4.262 Γ— 10⁹⁴(95-digit number)
42628826687569728794…18260336429635678129
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.525 Γ— 10⁹⁴(95-digit number)
85257653375139457588…36520672859271356259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.705 Γ— 10⁹⁡(96-digit number)
17051530675027891517…73041345718542712519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.410 Γ— 10⁹⁡(96-digit number)
34103061350055783035…46082691437085425039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.820 Γ— 10⁹⁡(96-digit number)
68206122700111566070…92165382874170850079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.364 Γ— 10⁹⁢(97-digit number)
13641224540022313214…84330765748341700159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.728 Γ— 10⁹⁢(97-digit number)
27282449080044626428…68661531496683400319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.456 Γ— 10⁹⁢(97-digit number)
54564898160089252856…37323062993366800639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁷(98-digit number)
10912979632017850571…74646125986733601279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.182 Γ— 10⁹⁷(98-digit number)
21825959264035701142…49292251973467202559
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:57,970,896 XPMΒ·at block #6,840,817 Β· updates every 60s
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