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Block #647,498

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2014, 4:01:54 PM Β· Difficulty 10.9514 Β· 6,161,607 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
105bd6b244c757505492891d232c849ce5173d6088e193a2f0994387facfe761
View on Chainz β†—

Height

#647,498

Difficulty

10.951446

Transactions

3

Size

658 B

Version

2

Bits

0af391fe

Nonce

504,714,993

Timestamp

7/25/2014, 4:01:54 PM

Confirmations

6,161,607

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

03782af24c93f931a95f374f9f3bb1be0183ef6c6683ce4227daf95ab185fa5a
Transactions (3)
Coinbased6f20f07950ad8…5635a4ac253334
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
eb82b3c50219ba…fef1820b178980
1 in β†’ 2 out8.3000 XPM226 B
AXhxnx2K…2RbJFRpDAe7ht6Sj…7i8cq412
58ba7c65ab24a6…e3990bd8513757
1 in β†’ 2 out3.0442 XPM225 B
ALtCY33p…AGUGHeMWAGAMt16a…4LVibYA3
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.

3.057 Γ— 10⁹⁷(98-digit number)
30579241530939017170…05029629313454202881
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
3.057 Γ— 10⁹⁷(98-digit number)
30579241530939017170…05029629313454202881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.115 Γ— 10⁹⁷(98-digit number)
61158483061878034341…10059258626908405761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.223 Γ— 10⁹⁸(99-digit number)
12231696612375606868…20118517253816811521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.446 Γ— 10⁹⁸(99-digit number)
24463393224751213736…40237034507633623041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.892 Γ— 10⁹⁸(99-digit number)
48926786449502427472…80474069015267246081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.785 Γ— 10⁹⁸(99-digit number)
97853572899004854945…60948138030534492161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.957 Γ— 10⁹⁹(100-digit number)
19570714579800970989…21896276061068984321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.914 Γ— 10⁹⁹(100-digit number)
39141429159601941978…43792552122137968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.828 Γ— 10⁹⁹(100-digit number)
78282858319203883956…87585104244275937281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.565 Γ— 10¹⁰⁰(101-digit number)
15656571663840776791…75170208488551874561
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:57,716,895 XPMΒ·at block #6,809,104 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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