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Block #644,939

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2014, 4:23:25 PM Β· Difficulty 10.9542 Β· 6,161,946 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d464d469c74d906782fa9341e2a239cf0899bee055c0e5ec89f8aadf0af5a73f
View on Chainz β†—

Height

#644,939

Difficulty

10.954164

Transactions

1

Size

207 B

Version

2

Bits

0af44410

Nonce

461,749,932

Timestamp

7/23/2014, 4:23:25 PM

Confirmations

6,161,946

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d25fef89c2e83bb221553987a29d7bbda9652ba6f1e518c33db4b2855f382d74
Transactions (1)
Coinbased25fef89c2e83b…b4b2855f382d74
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.744 Γ— 10⁹⁷(98-digit number)
57449938185938257066…99177459207806809601
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
5.744 Γ— 10⁹⁷(98-digit number)
57449938185938257066…99177459207806809601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.148 Γ— 10⁹⁸(99-digit number)
11489987637187651413…98354918415613619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.297 Γ— 10⁹⁸(99-digit number)
22979975274375302826…96709836831227238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.595 Γ— 10⁹⁸(99-digit number)
45959950548750605653…93419673662454476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.191 Γ— 10⁹⁸(99-digit number)
91919901097501211307…86839347324908953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.838 Γ— 10⁹⁹(100-digit number)
18383980219500242261…73678694649817907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.676 Γ— 10⁹⁹(100-digit number)
36767960439000484522…47357389299635814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.353 Γ— 10⁹⁹(100-digit number)
73535920878000969045…94714778599271628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.470 Γ— 10¹⁰⁰(101-digit number)
14707184175600193809…89429557198543257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.941 Γ— 10¹⁰⁰(101-digit number)
29414368351200387618…78859114397086515201
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:57,699,189 XPMΒ·at block #6,806,884 Β· updates every 60s
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