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Block #1,628,888

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/15/2016, 12:19:01 AM Β· Difficulty 10.6022 Β· 5,214,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44188faeb88b7c2c4ec174a712831b650a605eb15fd1e5f3e21a32f089dd075f
View on Chainz β†—

Height

#1,628,888

Difficulty

10.602197

Transactions

1

Size

201 B

Version

2

Bits

0a9a299c

Nonce

476,673,629

Timestamp

6/15/2016, 12:19:01 AM

Confirmations

5,214,101

Mined by

⛏️ P2SHAaH77PzpdcwsDYvSQPW6hKZdwkYVNxVbsX

Merkle Root

6a645b7aa385e720d9ec431736dd2b41be851da40493da8a9902853b9bac75d7
Transactions (1)
Coinbase6a645b7aa385e7…02853b9bac75d7
1 in β†’ 1 out8.8800 XPM110 B
AaH77Pzp…YVNxVbsX
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.

1.461 Γ— 10⁹⁢(97-digit number)
14618297146240905073…50149292502549605119
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
1.461 Γ— 10⁹⁢(97-digit number)
14618297146240905073…50149292502549605119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.923 Γ— 10⁹⁢(97-digit number)
29236594292481810146…00298585005099210239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.847 Γ— 10⁹⁢(97-digit number)
58473188584963620293…00597170010198420479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.169 Γ— 10⁹⁷(98-digit number)
11694637716992724058…01194340020396840959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.338 Γ— 10⁹⁷(98-digit number)
23389275433985448117…02388680040793681919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.677 Γ— 10⁹⁷(98-digit number)
46778550867970896235…04777360081587363839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.355 Γ— 10⁹⁷(98-digit number)
93557101735941792470…09554720163174727679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.871 Γ— 10⁹⁸(99-digit number)
18711420347188358494…19109440326349455359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.742 Γ— 10⁹⁸(99-digit number)
37422840694376716988…38218880652698910719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.484 Γ— 10⁹⁸(99-digit number)
74845681388753433976…76437761305397821439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,988,268 XPMΒ·at block #6,842,988 Β· updates every 60s
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