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Block #200,419

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/9/2013, 12:11:34 AM Β· Difficulty 9.8895 Β· 6,596,456 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e35b84915d94551cc902259933680d0480088c19bf50a22f4810791236d3333
View on Chainz β†—

Height

#200,419

Difficulty

9.889465

Transactions

2

Size

357 B

Version

2

Bits

09e3b3f4

Nonce

38,839

Timestamp

10/9/2013, 12:11:34 AM

Confirmations

6,596,456

Mined by

⛏️ P2SHARPU9skP7dKWz4Ka74pUfeVsjQDoRVGg3C

Merkle Root

702ee55f19d2b694b4be59d3ed84e7f732d21357202c13940e0b12c8bd51b1d7
Transactions (2)
Coinbase643c6110704940…b4a0bb371c2014
1 in β†’ 1 out10.2200 XPM109 B
ARPU9skP…DoRVGg3C
33a446c79ef746…40c1899cc74337
1 in β†’ 1 out10.2200 XPM158 B
AN7CTbAY…CXZXPsEU
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.

1.933 Γ— 10⁹⁴(95-digit number)
19334067736598844646…74013817372119665281
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
1.933 Γ— 10⁹⁴(95-digit number)
19334067736598844646…74013817372119665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.866 Γ— 10⁹⁴(95-digit number)
38668135473197689292…48027634744239330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.733 Γ— 10⁹⁴(95-digit number)
77336270946395378584…96055269488478661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.546 Γ— 10⁹⁡(96-digit number)
15467254189279075716…92110538976957322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.093 Γ— 10⁹⁡(96-digit number)
30934508378558151433…84221077953914644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.186 Γ— 10⁹⁡(96-digit number)
61869016757116302867…68442155907829288961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.237 Γ— 10⁹⁢(97-digit number)
12373803351423260573…36884311815658577921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.474 Γ— 10⁹⁢(97-digit number)
24747606702846521146…73768623631317155841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.949 Γ— 10⁹⁢(97-digit number)
49495213405693042293…47537247262634311681
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:57,619,016 XPMΒ·at block #6,796,874 Β· updates every 60s
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