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Block #2,117,255

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2017, 10:12:54 AM Β· Difficulty 10.9054 Β· 4,725,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ca4a844bdeac30bae188f99ae661deff7e7a3d4e6102a2661bd96e6f2dc2b86
View on Chainz β†—

Height

#2,117,255

Difficulty

10.905382

Transactions

1

Size

243 B

Version

2

Bits

0ae7c723

Nonce

1,534,086,922

Timestamp

5/15/2017, 10:12:54 AM

Confirmations

4,725,209

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

6e15bf2f73054043ad204d5a9ae8b72e2e6574bfa7edcee9f0d2b079d9c765d4
Transactions (1)
Coinbase6e15bf2f730540…d2b079d9c765d4
1 in β†’ 2 out8.4000 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

1.974 Γ— 10⁹⁢(97-digit number)
19741800704782341452…55644836837946417921
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
1.974 Γ— 10⁹⁢(97-digit number)
19741800704782341452…55644836837946417921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.948 Γ— 10⁹⁢(97-digit number)
39483601409564682904…11289673675892835841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.896 Γ— 10⁹⁢(97-digit number)
78967202819129365808…22579347351785671681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.579 Γ— 10⁹⁷(98-digit number)
15793440563825873161…45158694703571343361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.158 Γ— 10⁹⁷(98-digit number)
31586881127651746323…90317389407142686721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.317 Γ— 10⁹⁷(98-digit number)
63173762255303492646…80634778814285373441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.263 Γ— 10⁹⁸(99-digit number)
12634752451060698529…61269557628570746881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.526 Γ— 10⁹⁸(99-digit number)
25269504902121397058…22539115257141493761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.053 Γ— 10⁹⁸(99-digit number)
50539009804242794117…45078230514282987521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.010 Γ— 10⁹⁹(100-digit number)
10107801960848558823…90156461028565975041
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:57,984,130 XPMΒ·at block #6,842,463 Β· updates every 60s
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