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Block #1,534,374

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 4:58:57 AM Β· Difficulty 10.6171 Β· 5,292,782 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3374f3b53c7b92baa79c379336e4508093361518f3d8b6e6d95d7a0eb346ef0f
View on Chainz β†—

Height

#1,534,374

Difficulty

10.617097

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9dfa14

Nonce

756,830,715

Timestamp

4/10/2016, 4:58:57 AM

Confirmations

5,292,782

Mined by

⛏️ P2SHAPNoAhaFF7S4tCSXzFY8xWzwjqoYyLjeRM

Merkle Root

f8c9aa40be846a9a61208c6678a3de97e04e50612f0b84e0204eccc3673ce1f2
Transactions (2)
Coinbase9329e65e5a2db5…99cb1adac0e789
1 in β†’ 1 out8.9400 XPM109 B
APNoAhaF…oYyLjeRM
9f20c931e05522…6d2d14c769b1cd
51 in β†’ 1 out2692.5777 XPM7.41 KB
AacpBR9u…8mGnnUH2
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.

1.767 Γ— 10⁹⁡(96-digit number)
17677479528496973443…82387370912709495681
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
1.767 Γ— 10⁹⁡(96-digit number)
17677479528496973443…82387370912709495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.535 Γ— 10⁹⁡(96-digit number)
35354959056993946887…64774741825418991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.070 Γ— 10⁹⁡(96-digit number)
70709918113987893775…29549483650837982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.414 Γ— 10⁹⁢(97-digit number)
14141983622797578755…59098967301675965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.828 Γ— 10⁹⁢(97-digit number)
28283967245595157510…18197934603351930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.656 Γ— 10⁹⁢(97-digit number)
56567934491190315020…36395869206703861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.131 Γ— 10⁹⁷(98-digit number)
11313586898238063004…72791738413407723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.262 Γ— 10⁹⁷(98-digit number)
22627173796476126008…45583476826815447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.525 Γ— 10⁹⁷(98-digit number)
45254347592952252016…91166953653630894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.050 Γ— 10⁹⁷(98-digit number)
90508695185904504032…82333907307261788161
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:57,861,432 XPMΒ·at block #6,827,155 Β· updates every 60s
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