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Block #263,506

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2013, 9:25:47 PM Β· Difficulty 9.9660 Β· 6,578,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b6c0b32c6584bd59bb218642fc178c3aad8323d43ccc90bc2df0ba18baea5b95
View on Chainz β†—

Height

#263,506

Difficulty

9.965977

Transactions

1

Size

198 B

Version

2

Bits

09f74a4c

Nonce

282,069

Timestamp

11/17/2013, 9:25:47 PM

Confirmations

6,578,832

Mined by

⛏️ P2SHAGrJNSJ3hSHEqprpFW7VqE8aCawJgGsruL

Merkle Root

0949a1b4acf9f65fc836421418d611566a7d0b2f409ba6fd0efc8ee659ac5ad2
Transactions (1)
Coinbase0949a1b4acf9f6…fc8ee659ac5ad2
1 in β†’ 1 out10.0500 XPM109 B
AGrJNSJ3…wJgGsruL
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.

5.610 Γ— 10⁹²(93-digit number)
56104338007770444482…61959108776087109601
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
5.610 Γ— 10⁹²(93-digit number)
56104338007770444482…61959108776087109601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.122 Γ— 10⁹³(94-digit number)
11220867601554088896…23918217552174219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.244 Γ— 10⁹³(94-digit number)
22441735203108177792…47836435104348438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.488 Γ— 10⁹³(94-digit number)
44883470406216355585…95672870208696876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.976 Γ— 10⁹³(94-digit number)
89766940812432711171…91345740417393753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.795 Γ— 10⁹⁴(95-digit number)
17953388162486542234…82691480834787507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.590 Γ— 10⁹⁴(95-digit number)
35906776324973084468…65382961669575014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.181 Γ— 10⁹⁴(95-digit number)
71813552649946168937…30765923339150028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.436 Γ— 10⁹⁡(96-digit number)
14362710529989233787…61531846678300057601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.872 Γ— 10⁹⁡(96-digit number)
28725421059978467574…23063693356600115201
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:57,983,111 XPMΒ·at block #6,842,337 Β· updates every 60s
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