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Block #2,295,886

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2017, 11:23:21 AM Β· Difficulty 10.9512 Β· 4,535,655 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ca5dc0216f2e859ff56150799fdf0423e1f03f69e2b5d710506e37a3f05b293
View on Chainz β†—

Height

#2,295,886

Difficulty

10.951194

Transactions

2

Size

425 B

Version

2

Bits

0af38171

Nonce

891,691,735

Timestamp

9/14/2017, 11:23:21 AM

Confirmations

4,535,655

Mined by

⛏️ P2SHAXPKpPdp6BGhmvSvb5AFsdoMGcq3HxnAuT

Merkle Root

ec4c57f1e42db15b48d445e6dca0ff96ef77e0e8758f377b236e67204fad499a
Transactions (2)
Coinbasef9ffce6a071c98…804b9ccfffea07
1 in β†’ 1 out8.3300 XPM109 B
AXPKpPdp…q3HxnAuT
6a8dcef57839ff…8b6ba3643185db
1 in β†’ 2 out32658.0938 XPM226 B
AcfzcQ9L…VDCamTdjATcbvWF6…7XYUkWNR
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.

5.623 Γ— 10⁹⁴(95-digit number)
56237645711160469924…39375051805851562801
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
5.623 Γ— 10⁹⁴(95-digit number)
56237645711160469924…39375051805851562801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.124 Γ— 10⁹⁡(96-digit number)
11247529142232093984…78750103611703125601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.249 Γ— 10⁹⁡(96-digit number)
22495058284464187969…57500207223406251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.499 Γ— 10⁹⁡(96-digit number)
44990116568928375939…15000414446812502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.998 Γ— 10⁹⁡(96-digit number)
89980233137856751878…30000828893625004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.799 Γ— 10⁹⁢(97-digit number)
17996046627571350375…60001657787250009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.599 Γ— 10⁹⁢(97-digit number)
35992093255142700751…20003315574500019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.198 Γ— 10⁹⁢(97-digit number)
71984186510285401502…40006631149000038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.439 Γ— 10⁹⁷(98-digit number)
14396837302057080300…80013262298000076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.879 Γ— 10⁹⁷(98-digit number)
28793674604114160601…60026524596000153601
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:57,896,418 XPMΒ·at block #6,831,540 Β· updates every 60s
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