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Block #2,255,298

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/17/2017, 6:10:54 AM Β· Difficulty 10.9503 Β· 4,554,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c21d98c0c6102327387b797bbac02c436bf4abd8dbd00f3068857d33bd12ec0
View on Chainz β†—

Height

#2,255,298

Difficulty

10.950310

Transactions

1

Size

200 B

Version

2

Bits

0af34786

Nonce

1,445,030,588

Timestamp

8/17/2017, 6:10:54 AM

Confirmations

4,554,630

Mined by

⛏️ P2SHAXYZi3RhGvo5rEzLpakhyzUu64T2Jb6s18

Merkle Root

a172d6d2aa9686d22ac7f67163fec3ad31ee62cc9680a27c3407e6621521a030
Transactions (1)
Coinbasea172d6d2aa9686…07e6621521a030
1 in β†’ 1 out8.3300 XPM109 B
AXYZi3Rh…T2Jb6s18
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.

5.416 Γ— 10⁹⁢(97-digit number)
54162211032084038196…20580997686146754561
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
5.416 Γ— 10⁹⁢(97-digit number)
54162211032084038196…20580997686146754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.083 Γ— 10⁹⁷(98-digit number)
10832442206416807639…41161995372293509121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.166 Γ— 10⁹⁷(98-digit number)
21664884412833615278…82323990744587018241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.332 Γ— 10⁹⁷(98-digit number)
43329768825667230556…64647981489174036481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.665 Γ— 10⁹⁷(98-digit number)
86659537651334461113…29295962978348072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.733 Γ— 10⁹⁸(99-digit number)
17331907530266892222…58591925956696145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.466 Γ— 10⁹⁸(99-digit number)
34663815060533784445…17183851913392291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.932 Γ— 10⁹⁸(99-digit number)
69327630121067568891…34367703826784583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.386 Γ— 10⁹⁹(100-digit number)
13865526024213513778…68735407653569167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.773 Γ— 10⁹⁹(100-digit number)
27731052048427027556…37470815307138334721
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,723,510 XPMΒ·at block #6,809,927 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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