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Block #1,681,809

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 2:22:47 PM Β· Difficulty 10.7168 Β· 5,159,696 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
873723378791f70e87100e311ef14e2a48b2bc40a01821ab3755ea34aeaf3395
View on Chainz β†—

Height

#1,681,809

Difficulty

10.716833

Transactions

1

Size

200 B

Version

2

Bits

0ab7825e

Nonce

537,516,942

Timestamp

7/20/2016, 2:22:47 PM

Confirmations

5,159,696

Mined by

⛏️ P2SHASdXfbRPs5cEKaYuFaQ2eCiQv5GSyjrwga

Merkle Root

29a8a92101075996044d34ee5d3cfd7600e712b90aa952996276c444e59d7f5a
Transactions (1)
Coinbase29a8a921010759…76c444e59d7f5a
1 in β†’ 1 out8.6900 XPM109 B
ASdXfbRP…GSyjrwga
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.

9.754 Γ— 10⁹⁡(96-digit number)
97549902473883574376…95499672541161359361
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
9.754 Γ— 10⁹⁡(96-digit number)
97549902473883574376…95499672541161359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.950 Γ— 10⁹⁢(97-digit number)
19509980494776714875…90999345082322718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.901 Γ— 10⁹⁢(97-digit number)
39019960989553429750…81998690164645437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.803 Γ— 10⁹⁢(97-digit number)
78039921979106859500…63997380329290874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.560 Γ— 10⁹⁷(98-digit number)
15607984395821371900…27994760658581749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.121 Γ— 10⁹⁷(98-digit number)
31215968791642743800…55989521317163499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.243 Γ— 10⁹⁷(98-digit number)
62431937583285487600…11979042634326999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.248 Γ— 10⁹⁸(99-digit number)
12486387516657097520…23958085268653998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.497 Γ— 10⁹⁸(99-digit number)
24972775033314195040…47916170537307996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.994 Γ— 10⁹⁸(99-digit number)
49945550066628390080…95832341074615992321
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:57,976,419 XPMΒ·at block #6,841,504 Β· updates every 60s
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