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Block #3,049,269

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/12/2019, 4:15:37 AM Β· Difficulty 10.9961 Β· 3,791,420 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b1480d5c6ff0c814b87264821d5b5d5b8bd9446cb7fe443cce0fb09a3c13d6a5
View on Chainz β†—

Height

#3,049,269

Difficulty

10.996090

Transactions

1

Size

199 B

Version

2

Bits

0afeffbe

Nonce

155,121,703

Timestamp

2/12/2019, 4:15:37 AM

Confirmations

3,791,420

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

09a41d23fdc50170f601013b765e895e2c8add1439fb2239fb1f3ee618869ba1
Transactions (1)
Coinbase09a41d23fdc501…1f3ee618869ba1
1 in β†’ 1 out8.2600 XPM109 B
AUMQRepm…tAfKmdW1
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.

5.483 Γ— 10⁹⁴(95-digit number)
54833184055941976799…24809576700549639519
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
5.483 Γ— 10⁹⁴(95-digit number)
54833184055941976799…24809576700549639519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁡(96-digit number)
10966636811188395359…49619153401099279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.193 Γ— 10⁹⁡(96-digit number)
21933273622376790719…99238306802198558079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.386 Γ— 10⁹⁡(96-digit number)
43866547244753581439…98476613604397116159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.773 Γ— 10⁹⁡(96-digit number)
87733094489507162879…96953227208794232319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.754 Γ— 10⁹⁢(97-digit number)
17546618897901432575…93906454417588464639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.509 Γ— 10⁹⁢(97-digit number)
35093237795802865151…87812908835176929279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.018 Γ— 10⁹⁢(97-digit number)
70186475591605730303…75625817670353858559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁷(98-digit number)
14037295118321146060…51251635340707717119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.807 Γ— 10⁹⁷(98-digit number)
28074590236642292121…02503270681415434239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.614 Γ— 10⁹⁷(98-digit number)
56149180473284584243…05006541362830868479
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:57,969,851 XPMΒ·at block #6,840,688 Β· updates every 60s
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