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Block #1,895,310

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2016, 1:18:40 PM Β· Difficulty 10.7487 Β· 4,931,529 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
774d1a1fbaeed2e9a3d3b1b2fe1385657c83c80849797a4c40ceacccb4627089
View on Chainz β†—

Height

#1,895,310

Difficulty

10.748681

Transactions

2

Size

1.68 KB

Version

2

Bits

0abfa98a

Nonce

1,153,226,166

Timestamp

12/15/2016, 1:18:40 PM

Confirmations

4,931,529

Mined by

⛏️ P2SHAHedT1Nm6pa27fFT3NfHWGxKifbEN4hbko

Merkle Root

c4c4ee8ea686ade501c7258ec70908c159334ba0f2012142764025cd670c8d51
Transactions (2)
Coinbasec2ae78a3053fd9…9a68f43039cdc7
1 in β†’ 1 out8.6800 XPM109 B
AHedT1Nm…bEN4hbko
4e0bde3af35dbf…79480d592dd8b2
10 in β†’ 1 out29.0258 XPM1.49 KB
AccdiNFt…f5ktXD48
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.

4.853 Γ— 10⁹⁴(95-digit number)
48537029071222088262…62230168001151368161
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
4.853 Γ— 10⁹⁴(95-digit number)
48537029071222088262…62230168001151368161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.707 Γ— 10⁹⁴(95-digit number)
97074058142444176525…24460336002302736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.941 Γ— 10⁹⁡(96-digit number)
19414811628488835305…48920672004605472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.882 Γ— 10⁹⁡(96-digit number)
38829623256977670610…97841344009210945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.765 Γ— 10⁹⁡(96-digit number)
77659246513955341220…95682688018421890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.553 Γ— 10⁹⁢(97-digit number)
15531849302791068244…91365376036843781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.106 Γ— 10⁹⁢(97-digit number)
31063698605582136488…82730752073687562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.212 Γ— 10⁹⁢(97-digit number)
62127397211164272976…65461504147375124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.242 Γ— 10⁹⁷(98-digit number)
12425479442232854595…30923008294750248961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.485 Γ— 10⁹⁷(98-digit number)
24850958884465709190…61846016589500497921
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:57,858,879 XPMΒ·at block #6,826,838 Β· updates every 60s
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