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Block #83,657

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/26/2013, 7:34:59 AM Β· Difficulty 9.2676 Β· 6,722,399 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
395885ad1ab740086375ca55667d5f919b0ddc89b310a398934c8aa5e83210ed
View on Chainz β†—

Height

#83,657

Difficulty

9.267579

Transactions

1

Size

201 B

Version

2

Bits

09448008

Nonce

150,859

Timestamp

7/26/2013, 7:34:59 AM

Confirmations

6,722,399

Mined by

⛏️ P2SHAc3AUHowoddp8FyKEjyx2vqHMdhYeSm7Mw

Merkle Root

d2d3fff60ca8ed9f573fce58c939d3c253b1bd12cbde2b38275bc96380e1acc3
Transactions (1)
Coinbased2d3fff60ca8ed…5bc96380e1acc3
1 in β†’ 1 out11.6300 XPM109 B
Ac3AUHow…hYeSm7Mw
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.

7.570 Γ— 10⁹⁸(99-digit number)
75702930885654371546…39925770669692488801
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
7.570 Γ— 10⁹⁸(99-digit number)
75702930885654371546…39925770669692488801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.514 Γ— 10⁹⁹(100-digit number)
15140586177130874309…79851541339384977601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.028 Γ— 10⁹⁹(100-digit number)
30281172354261748618…59703082678769955201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.056 Γ— 10⁹⁹(100-digit number)
60562344708523497236…19406165357539910401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.211 Γ— 10¹⁰⁰(101-digit number)
12112468941704699447…38812330715079820801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.422 Γ— 10¹⁰⁰(101-digit number)
24224937883409398894…77624661430159641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.844 Γ— 10¹⁰⁰(101-digit number)
48449875766818797789…55249322860319283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.689 Γ— 10¹⁰⁰(101-digit number)
96899751533637595578…10498645720638566401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.937 Γ— 10¹⁰¹(102-digit number)
19379950306727519115…20997291441277132801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,692,531 XPMΒ·at block #6,806,055 Β· updates every 60s
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