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Block #2,825,740

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 11:00:52 AM Β· Difficulty 11.7110 Β· 4,016,357 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eb94a7301e91d911bd72389e44a66685892f4003438445770722a951acd86708
View on Chainz β†—

Height

#2,825,740

Difficulty

11.711043

Transactions

1

Size

200 B

Version

2

Bits

0bb606ef

Nonce

569,738,128

Timestamp

9/5/2018, 11:00:52 AM

Confirmations

4,016,357

Mined by

⛏️ P2SHAVVuWw6dyw4QDqh1kXcvEN8WymuURXaArN

Merkle Root

423d89208970bb2cf37b948d516a3bcb3ff6d55c54174e6d874d4e5fe590e1b6
Transactions (1)
Coinbase423d89208970bb…4d4e5fe590e1b6
1 in β†’ 1 out7.2800 XPM110 B
AVVuWw6d…uURXaArN
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.

5.077 Γ— 10⁹⁴(95-digit number)
50772525448769922531…63923260844071122479
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
5.077 Γ— 10⁹⁴(95-digit number)
50772525448769922531…63923260844071122479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁡(96-digit number)
10154505089753984506…27846521688142244959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.030 Γ— 10⁹⁡(96-digit number)
20309010179507969012…55693043376284489919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.061 Γ— 10⁹⁡(96-digit number)
40618020359015938025…11386086752568979839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.123 Γ— 10⁹⁡(96-digit number)
81236040718031876050…22772173505137959679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁢(97-digit number)
16247208143606375210…45544347010275919359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.249 Γ— 10⁹⁢(97-digit number)
32494416287212750420…91088694020551838719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.498 Γ— 10⁹⁢(97-digit number)
64988832574425500840…82177388041103677439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁷(98-digit number)
12997766514885100168…64354776082207354879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.599 Γ— 10⁹⁷(98-digit number)
25995533029770200336…28709552164414709759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.199 Γ— 10⁹⁷(98-digit number)
51991066059540400672…57419104328829419519
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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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