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Block #2,780,265

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2018, 12:50:14 PM Β· Difficulty 11.6498 Β· 4,053,524 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e4422f092a0efd3eed9c06e066a013860f91d80fd5aa20ee061c4ad5a1d0b20
View on Chainz β†—

Height

#2,780,265

Difficulty

11.649836

Transactions

2

Size

574 B

Version

2

Bits

0ba65ba2

Nonce

540,831,442

Timestamp

8/5/2018, 12:50:14 PM

Confirmations

4,053,524

Mined by

⛏️ P2SHASL3un9FUnqL2fUGLCDXzDeJ1C8ztZxta5

Merkle Root

76709a4f8c27a4e507e24276863a30c0fc4c98b230a2fbca3d2c2086cbb7d8e6
Transactions (2)
Coinbase71482103ca888c…2768516f15e263
1 in β†’ 1 out7.3700 XPM110 B
ASL3un9F…8ztZxta5
a1444347e56c6c…304b77fa743881
2 in β†’ 2 out10.0142 XPM374 B
AVtYukH5…Resb2uSTAKGxoSP8…8oH3hVLd
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.

3.463 Γ— 10⁹³(94-digit number)
34635682184192205584…52568939113916687359
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
3.463 Γ— 10⁹³(94-digit number)
34635682184192205584…52568939113916687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.927 Γ— 10⁹³(94-digit number)
69271364368384411168…05137878227833374719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁴(95-digit number)
13854272873676882233…10275756455666749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.770 Γ— 10⁹⁴(95-digit number)
27708545747353764467…20551512911333498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.541 Γ— 10⁹⁴(95-digit number)
55417091494707528935…41103025822666997759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁡(96-digit number)
11083418298941505787…82206051645333995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.216 Γ— 10⁹⁡(96-digit number)
22166836597883011574…64412103290667991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.433 Γ— 10⁹⁡(96-digit number)
44333673195766023148…28824206581335982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.866 Γ— 10⁹⁡(96-digit number)
88667346391532046296…57648413162671964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.773 Γ— 10⁹⁢(97-digit number)
17733469278306409259…15296826325343928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.546 Γ— 10⁹⁢(97-digit number)
35466938556612818518…30593652650687856639
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:57,914,532 XPMΒ·at block #6,833,788 Β· updates every 60s
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