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Block #2,095,688

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2017, 11:58:15 AM Β· Difficulty 10.8716 Β· 4,737,774 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
924e66e2112a9ca164fb111381d5fad449ac9d56c1ef97005f44e6ddfdd67027
View on Chainz β†—

Height

#2,095,688

Difficulty

10.871571

Transactions

2

Size

4.28 KB

Version

2

Bits

0adf1f3f

Nonce

866,157,273

Timestamp

5/1/2017, 11:58:15 AM

Confirmations

4,737,774

Mined by

⛏️ P2SHALmyWdgkW1Sbc2VoLxrE2TsU5mU5A6VhXS

Merkle Root

ff9bcc3aaa8b69c7afc4848b54b9faa3f689d4a75213cff914a50227c16c8253
Transactions (2)
Coinbasecea12274ff055c…974a15122b3218
1 in β†’ 1 out8.5000 XPM109 B
ALmyWdgk…U5A6VhXS
de17c8e2c21021…281b1f77baf897
28 in β†’ 1 out130.4338 XPM4.09 KB
AFpHJhDK…hyA1PvSQ
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.

1.026 Γ— 10⁹³(94-digit number)
10264618828314593225…62690880567385938721
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
1.026 Γ— 10⁹³(94-digit number)
10264618828314593225…62690880567385938721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.052 Γ— 10⁹³(94-digit number)
20529237656629186451…25381761134771877441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.105 Γ— 10⁹³(94-digit number)
41058475313258372903…50763522269543754881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.211 Γ— 10⁹³(94-digit number)
82116950626516745806…01527044539087509761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.642 Γ— 10⁹⁴(95-digit number)
16423390125303349161…03054089078175019521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.284 Γ— 10⁹⁴(95-digit number)
32846780250606698322…06108178156350039041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.569 Γ— 10⁹⁴(95-digit number)
65693560501213396644…12216356312700078081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.313 Γ— 10⁹⁡(96-digit number)
13138712100242679328…24432712625400156161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.627 Γ— 10⁹⁡(96-digit number)
26277424200485358657…48865425250800312321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.255 Γ— 10⁹⁡(96-digit number)
52554848400970717315…97730850501600624641
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:57,911,896 XPMΒ·at block #6,833,461 Β· updates every 60s
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