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Block #3,274,970

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2019, 10:12:02 PM Β· Difficulty 10.9952 Β· 3,557,614 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d0fd814642ea49f602f23995c67d381ddbae5030eb456741be805b905dfe486
View on Chainz β†—

Height

#3,274,970

Difficulty

10.995213

Transactions

1

Size

200 B

Version

2

Bits

0afec64b

Nonce

1,793,040,632

Timestamp

7/20/2019, 10:12:02 PM

Confirmations

3,557,614

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

037d4446f2db74ab8153ca2868718f2855afff088a4f27b8bab28af90781336d
Transactions (1)
Coinbase037d4446f2db74…b28af90781336d
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.346 Γ— 10⁹⁡(96-digit number)
23469544135296706669…77778313649415497919
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
2.346 Γ— 10⁹⁡(96-digit number)
23469544135296706669…77778313649415497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.693 Γ— 10⁹⁡(96-digit number)
46939088270593413338…55556627298830995839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.387 Γ— 10⁹⁡(96-digit number)
93878176541186826677…11113254597661991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.877 Γ— 10⁹⁢(97-digit number)
18775635308237365335…22226509195323983359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.755 Γ— 10⁹⁢(97-digit number)
37551270616474730670…44453018390647966719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.510 Γ— 10⁹⁢(97-digit number)
75102541232949461341…88906036781295933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.502 Γ— 10⁹⁷(98-digit number)
15020508246589892268…77812073562591866879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.004 Γ— 10⁹⁷(98-digit number)
30041016493179784536…55624147125183733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.008 Γ— 10⁹⁷(98-digit number)
60082032986359569073…11248294250367467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.201 Γ— 10⁹⁸(99-digit number)
12016406597271913814…22496588500734935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.403 Γ— 10⁹⁸(99-digit number)
24032813194543827629…44993177001469870079
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:57,904,820 XPMΒ·at block #6,832,583 Β· updates every 60s
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