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Block #3,335,253

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2019, 6:23:27 PM Β· Difficulty 11.0018 Β· 3,507,612 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49776ec71b87df6dbc16ed6b29220444b92e1bda2b472f67bf4ff01e6be2d709
View on Chainz β†—

Height

#3,335,253

Difficulty

11.001781

Transactions

2

Size

576 B

Version

2

Bits

0b0074be

Nonce

983,456,713

Timestamp

8/31/2019, 6:23:27 PM

Confirmations

3,507,612

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2876596c1d25e1153305fc993666155970a13b0dbd38b14034dbdd0cec3f9c8d
Transactions (2)
Coinbase148f8f031ab452…1b0e6da84bfa15
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
d0c761317269a4…f90e57263d749f
2 in β†’ 2 out66.7271 XPM376 B
AeTHTL7A…vT1872bkAGKFJUQz…PJu6KAKA
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.

4.799 Γ— 10⁹⁡(96-digit number)
47996920155546954671…08403402551334816319
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
4.799 Γ— 10⁹⁡(96-digit number)
47996920155546954671…08403402551334816319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.599 Γ— 10⁹⁡(96-digit number)
95993840311093909343…16806805102669632639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.919 Γ— 10⁹⁢(97-digit number)
19198768062218781868…33613610205339265279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.839 Γ— 10⁹⁢(97-digit number)
38397536124437563737…67227220410678530559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.679 Γ— 10⁹⁢(97-digit number)
76795072248875127475…34454440821357061119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.535 Γ— 10⁹⁷(98-digit number)
15359014449775025495…68908881642714122239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.071 Γ— 10⁹⁷(98-digit number)
30718028899550050990…37817763285428244479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.143 Γ— 10⁹⁷(98-digit number)
61436057799100101980…75635526570856488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.228 Γ— 10⁹⁸(99-digit number)
12287211559820020396…51271053141712977919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.457 Γ— 10⁹⁸(99-digit number)
24574423119640040792…02542106283425955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.914 Γ— 10⁹⁸(99-digit number)
49148846239280081584…05084212566851911679
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:57,987,266 XPMΒ·at block #6,842,864 Β· updates every 60s
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