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Block #210,145

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/14/2013, 11:12:10 PM Β· Difficulty 9.9125 Β· 6,597,966 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
55d8ebeb56ae807065eb01f4cd42bc629eb002b79a2f3696fe7a2ec43588e04c
View on Chainz β†—

Height

#210,145

Difficulty

9.912491

Transactions

2

Size

721 B

Version

2

Bits

09e99906

Nonce

3,620

Timestamp

10/14/2013, 11:12:10 PM

Confirmations

6,597,966

Mined by

⛏️ P2SHAaC7FfYJ3wgrxGC78ZvTmB5mToNd6BeiX3

Merkle Root

227e4f485840aeacbcaa0a74eee485ffd37f28a19233302e2e185b71fa1a8f9c
Transactions (2)
Coinbasefbb8311c8ac44f…c1f6678c492bc5
1 in β†’ 1 out10.1700 XPM109 B
AaC7FfYJ…Nd6BeiX3
daa6965cc0ff4b…4597ed3a76d0ed
3 in β†’ 2 out9.9113 XPM522 B
AJgP92fN…X87VRLAKAQN4gRo8…ne3f5au4
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.

2.988 Γ— 10⁹⁴(95-digit number)
29888620795471085618…52660230317297185921
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
2.988 Γ— 10⁹⁴(95-digit number)
29888620795471085618…52660230317297185921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.977 Γ— 10⁹⁴(95-digit number)
59777241590942171237…05320460634594371841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11955448318188434247…10640921269188743681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.391 Γ— 10⁹⁡(96-digit number)
23910896636376868494…21281842538377487361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.782 Γ— 10⁹⁡(96-digit number)
47821793272753736989…42563685076754974721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.564 Γ— 10⁹⁡(96-digit number)
95643586545507473979…85127370153509949441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.912 Γ— 10⁹⁢(97-digit number)
19128717309101494795…70254740307019898881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.825 Γ— 10⁹⁢(97-digit number)
38257434618202989591…40509480614039797761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.651 Γ— 10⁹⁢(97-digit number)
76514869236405979183…81018961228079595521
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:57,708,935 XPMΒ·at block #6,808,110 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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