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Block #633,507

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2014, 9:07:58 PM Β· Difficulty 10.9639 Β· 6,182,542 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c13d27f7398a6c2f7367812c1a95630d908d8036622d2bd6224c80b8f4a14698
View on Chainz β†—

Height

#633,507

Difficulty

10.963865

Transactions

2

Size

8.37 KB

Version

2

Bits

0af6bfde

Nonce

383,127,443

Timestamp

7/14/2014, 9:07:58 PM

Confirmations

6,182,542

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

902cb2e8056ce7c5cb9b65f837aee52b8395d6befa16f4c584616af37f612083
Transactions (2)
Coinbase81650da0c83f2c…2c581088e4365a
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
f5cfb7d18cd7fd…7eee3de7fd0889
56 in β†’ 2 out30.1536 XPM8.17 KB
ALnCb6L3…WzVjspMQAPP97DSB…Wfj7mmNu
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.

6.597 Γ— 10⁹⁡(96-digit number)
65976898915580974755…99678065866581309921
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
6.597 Γ— 10⁹⁡(96-digit number)
65976898915580974755…99678065866581309921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.319 Γ— 10⁹⁢(97-digit number)
13195379783116194951…99356131733162619841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.639 Γ— 10⁹⁢(97-digit number)
26390759566232389902…98712263466325239681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.278 Γ— 10⁹⁢(97-digit number)
52781519132464779804…97424526932650479361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.055 Γ— 10⁹⁷(98-digit number)
10556303826492955960…94849053865300958721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.111 Γ— 10⁹⁷(98-digit number)
21112607652985911921…89698107730601917441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.222 Γ— 10⁹⁷(98-digit number)
42225215305971823843…79396215461203834881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.445 Γ— 10⁹⁷(98-digit number)
84450430611943647686…58792430922407669761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.689 Γ— 10⁹⁸(99-digit number)
16890086122388729537…17584861844815339521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.378 Γ— 10⁹⁸(99-digit number)
33780172244777459074…35169723689630679041
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:57,772,506 XPMΒ·at block #6,816,048 Β· updates every 60s
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