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Block #303,903

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/10/2013, 3:21:58 PM Β· Difficulty 9.9932 Β· 6,520,655 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8539f74c7c1e5db17d7db28808dbd6327585b43e636df96bcff0db61e1b563cb
View on Chainz β†—

Height

#303,903

Difficulty

9.993171

Transactions

1

Size

207 B

Version

2

Bits

09fe406e

Nonce

147,111

Timestamp

12/10/2013, 3:21:58 PM

Confirmations

6,520,655

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4ce3a39f8a23d4773d4d74ca4637cf5407cec2c5bc7f888d4188be84748559ee
Transactions (1)
Coinbase4ce3a39f8a23d4…88be84748559ee
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

7.042 Γ— 10⁹⁢(97-digit number)
70429385879477739179…75482905454493378561
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
7.042 Γ— 10⁹⁢(97-digit number)
70429385879477739179…75482905454493378561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.408 Γ— 10⁹⁷(98-digit number)
14085877175895547835…50965810908986757121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.817 Γ— 10⁹⁷(98-digit number)
28171754351791095671…01931621817973514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.634 Γ— 10⁹⁷(98-digit number)
56343508703582191343…03863243635947028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.126 Γ— 10⁹⁸(99-digit number)
11268701740716438268…07726487271894056961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.253 Γ— 10⁹⁸(99-digit number)
22537403481432876537…15452974543788113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.507 Γ— 10⁹⁸(99-digit number)
45074806962865753074…30905949087576227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.014 Γ— 10⁹⁸(99-digit number)
90149613925731506149…61811898175152455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.802 Γ— 10⁹⁹(100-digit number)
18029922785146301229…23623796350304911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.605 Γ— 10⁹⁹(100-digit number)
36059845570292602459…47247592700609822721
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:57,840,528 XPMΒ·at block #6,824,557 Β· updates every 60s
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