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Block #53,951

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 5:56:08 PM Β· Difficulty 8.9288 Β· 6,741,109 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22c92ac9ef27446fa879d59a1e9f6db589f6b93fb88539a8e398314fbcf1d696
View on Chainz β†—

Height

#53,951

Difficulty

8.928785

Transactions

3

Size

515 B

Version

2

Bits

08edc4de

Nonce

257

Timestamp

7/16/2013, 5:56:08 PM

Confirmations

6,741,109

Mined by

⛏️ P2SHAGY4TBx7s42EHEAbrwoVx7JoxEYfD8h7Va

Merkle Root

d8d06287b6dc9e08ae9eeccb91f2d8ef47f2f7e4d510d464320b9e3f422f1979
Transactions (3)
Coinbase51d08b2d72d25c…72b01c62542e98
1 in β†’ 1 out12.5500 XPM110 B
AGY4TBx7…YfD8h7Va
3ef7f42b11d804…15cc52ec5a799b
1 in β†’ 1 out13.3000 XPM158 B
Af72phx2…8eoFuBNY
8ac05cf467625b…ff4ae8d553ef41
1 in β†’ 1 out12.8400 XPM157 B
Af72phx2…8eoFuBNY
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.

9.050 Γ— 10⁹⁴(95-digit number)
90508896157681826642…94547115304436091001
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
9.050 Γ— 10⁹⁴(95-digit number)
90508896157681826642…94547115304436091001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.810 Γ— 10⁹⁡(96-digit number)
18101779231536365328…89094230608872182001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.620 Γ— 10⁹⁡(96-digit number)
36203558463072730656…78188461217744364001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.240 Γ— 10⁹⁡(96-digit number)
72407116926145461313…56376922435488728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.448 Γ— 10⁹⁢(97-digit number)
14481423385229092262…12753844870977456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.896 Γ— 10⁹⁢(97-digit number)
28962846770458184525…25507689741954912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.792 Γ— 10⁹⁢(97-digit number)
57925693540916369051…51015379483909824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.158 Γ— 10⁹⁷(98-digit number)
11585138708183273810…02030758967819648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.317 Γ— 10⁹⁷(98-digit number)
23170277416366547620…04061517935639296001
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:57,604,521 XPMΒ·at block #6,795,059 Β· updates every 60s
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