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Block #1,682,200

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 8:14:50 PM Β· Difficulty 10.7190 Β· 5,157,431 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
58c24d7a83484f78ad28cf6ebd1ef18c6d5dfcdb8ce0d4eb08eae09993577eee
View on Chainz β†—

Height

#1,682,200

Difficulty

10.718981

Transactions

1

Size

200 B

Version

2

Bits

0ab80f2a

Nonce

302,577,968

Timestamp

7/20/2016, 8:14:50 PM

Confirmations

5,157,431

Mined by

⛏️ P2SHAHBWjWYVdHWzD5h7kDoXfD52Fd1ptB4Rnq

Merkle Root

a9ff20281645c8ab59a178aae76697510112ec59a92f4337e6ad2937b8f13641
Transactions (1)
Coinbasea9ff20281645c8…ad2937b8f13641
1 in β†’ 1 out8.6900 XPM109 B
AHBWjWYV…1ptB4Rnq
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.

1.590 Γ— 10⁹⁢(97-digit number)
15902501888217515929…53886820340636305921
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
1.590 Γ— 10⁹⁢(97-digit number)
15902501888217515929…53886820340636305921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.180 Γ— 10⁹⁢(97-digit number)
31805003776435031858…07773640681272611841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.361 Γ— 10⁹⁢(97-digit number)
63610007552870063716…15547281362545223681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.272 Γ— 10⁹⁷(98-digit number)
12722001510574012743…31094562725090447361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.544 Γ— 10⁹⁷(98-digit number)
25444003021148025486…62189125450180894721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.088 Γ— 10⁹⁷(98-digit number)
50888006042296050973…24378250900361789441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.017 Γ— 10⁹⁸(99-digit number)
10177601208459210194…48756501800723578881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.035 Γ— 10⁹⁸(99-digit number)
20355202416918420389…97513003601447157761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.071 Γ— 10⁹⁸(99-digit number)
40710404833836840778…95026007202894315521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.142 Γ— 10⁹⁸(99-digit number)
81420809667673681557…90052014405788631041
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:57,961,341 XPMΒ·at block #6,839,630 Β· updates every 60s
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