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Block #220,459

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 1:02:31 AM Β· Difficulty 9.9364 Β· 6,592,401 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51bc341b6437118b0ea5c2314ecb80d1acfa8d5fccf0009d88b66c3bcf758951
View on Chainz β†—

Height

#220,459

Difficulty

9.936355

Transactions

1

Size

198 B

Version

2

Bits

09efb4f1

Nonce

17,219

Timestamp

10/21/2013, 1:02:31 AM

Confirmations

6,592,401

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

9f662e9c7375efcc1a5f4d264307847af1f69621287eee506560d89ae7e9c4fe
Transactions (1)
Coinbase9f662e9c7375ef…60d89ae7e9c4fe
1 in β†’ 1 out10.1100 XPM109 B
AKgiTbag…MJA8ujWZ
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.

1.977 Γ— 10⁹³(94-digit number)
19775662753533731449…96258889583979812481
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
1.977 Γ— 10⁹³(94-digit number)
19775662753533731449…96258889583979812481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.955 Γ— 10⁹³(94-digit number)
39551325507067462898…92517779167959624961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.910 Γ— 10⁹³(94-digit number)
79102651014134925796…85035558335919249921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.582 Γ— 10⁹⁴(95-digit number)
15820530202826985159…70071116671838499841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.164 Γ— 10⁹⁴(95-digit number)
31641060405653970318…40142233343676999681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.328 Γ— 10⁹⁴(95-digit number)
63282120811307940636…80284466687353999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.265 Γ— 10⁹⁡(96-digit number)
12656424162261588127…60568933374707998721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.531 Γ— 10⁹⁡(96-digit number)
25312848324523176254…21137866749415997441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.062 Γ— 10⁹⁡(96-digit number)
50625696649046352509…42275733498831994881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,746,917 XPMΒ·at block #6,812,859 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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