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Block #663,023

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2014, 1:21:54 AM Β· Difficulty 10.9571 Β· 6,149,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b185aa7d8c4e682f7104f1f61aac386b590a1ff70f1c6d557fcd2251e1d12809
View on Chainz β†—

Height

#663,023

Difficulty

10.957069

Transactions

2

Size

425 B

Version

2

Bits

0af50280

Nonce

83,190

Timestamp

8/5/2014, 1:21:54 AM

Confirmations

6,149,532

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

d3a1e1b285ec0c8440fc8e666683e440772b4012799de8fc8ae53b6b6537459e
Transactions (2)
Coinbase9424a08b8f1a6e…91dd5703d98042
1 in β†’ 1 out8.3300 XPM109 B
ARaPyHgj…nA9veLYH
08a5fc317c08f0…4db0f2d92a0d94
1 in β†’ 2 out6.2208 XPM226 B
Ae7ht6Sj…7i8cq412AScUGn3Q…8Mg1KhAD
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.

8.582 Γ— 10⁹⁴(95-digit number)
85826567886451976455…69227247059334033601
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
8.582 Γ— 10⁹⁴(95-digit number)
85826567886451976455…69227247059334033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.716 Γ— 10⁹⁡(96-digit number)
17165313577290395291…38454494118668067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.433 Γ— 10⁹⁡(96-digit number)
34330627154580790582…76908988237336134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.866 Γ— 10⁹⁡(96-digit number)
68661254309161581164…53817976474672268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.373 Γ— 10⁹⁢(97-digit number)
13732250861832316232…07635952949344537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.746 Γ— 10⁹⁢(97-digit number)
27464501723664632465…15271905898689075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.492 Γ— 10⁹⁢(97-digit number)
54929003447329264931…30543811797378150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.098 Γ— 10⁹⁷(98-digit number)
10985800689465852986…61087623594756300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.197 Γ— 10⁹⁷(98-digit number)
21971601378931705972…22175247189512601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.394 Γ— 10⁹⁷(98-digit number)
43943202757863411945…44350494379025203201
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:57,744,473 XPMΒ·at block #6,812,554 Β· updates every 60s
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