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Block #2,083,288

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/22/2017, 9:08:55 PM Β· Difficulty 10.8714 Β· 4,743,633 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b9954600dbcda854831e443a02adb8ac8997ab3262f87ea71515800e8cca5a4e
View on Chainz β†—

Height

#2,083,288

Difficulty

10.871393

Transactions

2

Size

5.61 KB

Version

2

Bits

0adf13a0

Nonce

919,399,788

Timestamp

4/22/2017, 9:08:55 PM

Confirmations

4,743,633

Mined by

⛏️ P2SHASVb6iSqnN796Wrir2dqxS5Cx7b3BvRbRw

Merkle Root

fc47ef8c0ffb8899be6f8f4321c6f7600d360ceeebbcf0f0ee165761661b9e81
Transactions (2)
Coinbase89e7e268fb568a…e151a24f1b288b
1 in β†’ 1 out8.5100 XPM109 B
ASVb6iSq…b3BvRbRw
a06411ccad35da…4e5a3d5e83f143
37 in β†’ 2 out39.9999 XPM5.42 KB
AePPR69D…yL5adp7bAVikjw69…S7VnMeKw
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.

1.059 Γ— 10⁹⁴(95-digit number)
10599616815789844586…98374877892443727141
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
1.059 Γ— 10⁹⁴(95-digit number)
10599616815789844586…98374877892443727141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.119 Γ— 10⁹⁴(95-digit number)
21199233631579689173…96749755784887454281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.239 Γ— 10⁹⁴(95-digit number)
42398467263159378346…93499511569774908561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.479 Γ— 10⁹⁴(95-digit number)
84796934526318756693…86999023139549817121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.695 Γ— 10⁹⁡(96-digit number)
16959386905263751338…73998046279099634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.391 Γ— 10⁹⁡(96-digit number)
33918773810527502677…47996092558199268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.783 Γ— 10⁹⁡(96-digit number)
67837547621055005354…95992185116398536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.356 Γ— 10⁹⁢(97-digit number)
13567509524211001070…91984370232797073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.713 Γ— 10⁹⁢(97-digit number)
27135019048422002141…83968740465594147841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.427 Γ— 10⁹⁢(97-digit number)
54270038096844004283…67937480931188295681
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:57,859,539 XPMΒ·at block #6,826,920 Β· updates every 60s
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