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Block #1,756,372

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2016, 11:08:05 AM Β· Difficulty 10.7124 Β· 5,051,844 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
59f0ae56f93d698c0308108de1c9f59a310e1c42afdfde8578a97690da5bab94
View on Chainz β†—

Height

#1,756,372

Difficulty

10.712414

Transactions

2

Size

540 B

Version

2

Bits

0ab660bf

Nonce

1,411,781,189

Timestamp

9/10/2016, 11:08:05 AM

Confirmations

5,051,844

Mined by

⛏️ P2SHAKxgW8KSDS1B5B4WWa6yFzRQwKKXtBp6dM

Merkle Root

6539db092bff08c5aa55b1af6937f042fe2d75fb62ecef60012a0c9a42724b69
Transactions (2)
Coinbasee9a3b24c1f49d7…0d72305f3a1f9b
1 in β†’ 1 out8.7100 XPM110 B
AKxgW8KS…KXtBp6dM
e4bab0ca013139…3b79ca2680e99f
2 in β†’ 1 out10000.0000 XPM340 B
AYKArr5V…V9VqiqCZ
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.

3.456 Γ— 10⁹⁴(95-digit number)
34565866437310694609…60276316228977379121
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
3.456 Γ— 10⁹⁴(95-digit number)
34565866437310694609…60276316228977379121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.913 Γ— 10⁹⁴(95-digit number)
69131732874621389219…20552632457954758241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.382 Γ— 10⁹⁡(96-digit number)
13826346574924277843…41105264915909516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.765 Γ— 10⁹⁡(96-digit number)
27652693149848555687…82210529831819032961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.530 Γ— 10⁹⁡(96-digit number)
55305386299697111375…64421059663638065921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.106 Γ— 10⁹⁢(97-digit number)
11061077259939422275…28842119327276131841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.212 Γ— 10⁹⁢(97-digit number)
22122154519878844550…57684238654552263681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.424 Γ— 10⁹⁢(97-digit number)
44244309039757689100…15368477309104527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.848 Γ— 10⁹⁢(97-digit number)
88488618079515378200…30736954618209054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.769 Γ— 10⁹⁷(98-digit number)
17697723615903075640…61473909236418109441
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:57,709,780 XPMΒ·at block #6,808,215 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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