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Block #2,131,895

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 10:20:46 AM Β· Difficulty 10.9101 Β· 4,711,128 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57b6f0c39c6e475fcb6074a8882cbe3d3cfe658f3eeebf7d65b146f936d6e661
View on Chainz β†—

Height

#2,131,895

Difficulty

10.910147

Transactions

1

Size

200 B

Version

2

Bits

0ae8ff61

Nonce

732,727,640

Timestamp

5/25/2017, 10:20:46 AM

Confirmations

4,711,128

Mined by

⛏️ P2SHAWypePnv6iYVqo5yjSVfPPhpooZafznhr8

Merkle Root

b6c88c88efffe619055e909e5323c6bf882286c61dd1940a39ee9641f1745cbc
Transactions (1)
Coinbaseb6c88c88efffe6…ee9641f1745cbc
1 in β†’ 1 out8.3900 XPM109 B
AWypePnv…Zafznhr8
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.

1.739 Γ— 10⁹⁢(97-digit number)
17391126699159002047…36422090998980162561
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
1.739 Γ— 10⁹⁢(97-digit number)
17391126699159002047…36422090998980162561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.478 Γ— 10⁹⁢(97-digit number)
34782253398318004094…72844181997960325121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.956 Γ— 10⁹⁢(97-digit number)
69564506796636008189…45688363995920650241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.391 Γ— 10⁹⁷(98-digit number)
13912901359327201637…91376727991841300481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.782 Γ— 10⁹⁷(98-digit number)
27825802718654403275…82753455983682600961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.565 Γ— 10⁹⁷(98-digit number)
55651605437308806551…65506911967365201921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.113 Γ— 10⁹⁸(99-digit number)
11130321087461761310…31013823934730403841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.226 Γ— 10⁹⁸(99-digit number)
22260642174923522620…62027647869460807681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.452 Γ— 10⁹⁸(99-digit number)
44521284349847045241…24055295738921615361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.904 Γ— 10⁹⁸(99-digit number)
89042568699694090482…48110591477843230721
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:57,988,537 XPMΒ·at block #6,843,022 Β· updates every 60s
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