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Block #257,963

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/12/2013, 6:50:41 PM Β· Difficulty 9.9761 Β· 6,545,314 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db9958ab66a78bbeb8e85f180b66c327e4568d40949d7471b1c3a27d27c58fc6
View on Chainz β†—

Height

#257,963

Difficulty

9.976081

Transactions

2

Size

1.14 KB

Version

2

Bits

09f9e070

Nonce

7,510

Timestamp

11/12/2013, 6:50:41 PM

Confirmations

6,545,314

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

e43e7da865f81cb0b2b50eef59e51c3615092756c4d27a455a134ae0f17cefa5
Transactions (2)
Coinbaseb59f7094f416b9…b4d62c0b32c7ba
1 in β†’ 2 out10.0400 XPM142 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
743250a88791dc…8424db83401465
6 in β†’ 1 out100.4301 XPM932 B
AH5JF7V2…eR1hXcjP
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.

7.150 Γ— 10⁹⁴(95-digit number)
71502599879742162747…76547487184946033021
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
7.150 Γ— 10⁹⁴(95-digit number)
71502599879742162747…76547487184946033021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.430 Γ— 10⁹⁡(96-digit number)
14300519975948432549…53094974369892066041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.860 Γ— 10⁹⁡(96-digit number)
28601039951896865099…06189948739784132081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.720 Γ— 10⁹⁡(96-digit number)
57202079903793730198…12379897479568264161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.144 Γ— 10⁹⁢(97-digit number)
11440415980758746039…24759794959136528321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.288 Γ— 10⁹⁢(97-digit number)
22880831961517492079…49519589918273056641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.576 Γ— 10⁹⁢(97-digit number)
45761663923034984158…99039179836546113281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.152 Γ— 10⁹⁢(97-digit number)
91523327846069968316…98078359673092226561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.830 Γ— 10⁹⁷(98-digit number)
18304665569213993663…96156719346184453121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.660 Γ— 10⁹⁷(98-digit number)
36609331138427987326…92313438692368906241
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:57,670,242 XPMΒ·at block #6,803,276 Β· updates every 60s
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