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Block #3,085,439

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 1:22:28 PM Β· Difficulty 11.0303 Β· 3,757,089 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0866ae46a8a6474914004ca2c05e1d24aaf7c0d3d57cf28b4658dac7086ec33f
View on Chainz β†—

Height

#3,085,439

Difficulty

11.030343

Transactions

2

Size

2.59 KB

Version

2

Bits

0b07c495

Nonce

67,990,236

Timestamp

3/9/2019, 1:22:28 PM

Confirmations

3,757,089

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

8125c77d8e3496c25790c99c46c6d2a1b2d1b6c74accc3274564bbed135ae29a
Transactions (2)
Coinbasebbff6a8aa0df35…45dcbb4daba1fb
1 in β†’ 1 out8.2400 XPM110 B
AbXwmGxD…4XXYP765
a5ba94faaf3aa4…3edaf9f4260039
16 in β†’ 2 out2883.1720 XPM2.39 KB
AaBnRC14…ACmNV8D9AKxvgX5N…VQofZfAf
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.

6.428 Γ— 10⁹³(94-digit number)
64280935939681771795…12478854291535183999
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
6.428 Γ— 10⁹³(94-digit number)
64280935939681771795…12478854291535183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁴(95-digit number)
12856187187936354359…24957708583070367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁴(95-digit number)
25712374375872708718…49915417166140735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.142 Γ— 10⁹⁴(95-digit number)
51424748751745417436…99830834332281471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁡(96-digit number)
10284949750349083487…99661668664562943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.056 Γ— 10⁹⁡(96-digit number)
20569899500698166974…99323337329125887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.113 Γ— 10⁹⁡(96-digit number)
41139799001396333948…98646674658251775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.227 Γ— 10⁹⁡(96-digit number)
82279598002792667897…97293349316503551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁢(97-digit number)
16455919600558533579…94586698633007103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.291 Γ— 10⁹⁢(97-digit number)
32911839201117067159…89173397266014207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.582 Γ— 10⁹⁢(97-digit number)
65823678402234134318…78346794532028415999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,984,646 XPMΒ·at block #6,842,527 Β· updates every 60s
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