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Block #2,150,283

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/7/2017, 3:01:16 PM Β· Difficulty 10.8991 Β· 4,691,008 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8fb4ce1d5bace0b1453723ac48e353b4738b85a06421bf58abe671ed8a672afb
View on Chainz β†—

Height

#2,150,283

Difficulty

10.899065

Transactions

2

Size

424 B

Version

2

Bits

0ae62926

Nonce

1,779,230,520

Timestamp

6/7/2017, 3:01:16 PM

Confirmations

4,691,008

Mined by

⛏️ P2SHAZagjC2GmNoEZrZ3jvp3ujr1Xy9URube8X

Merkle Root

bf241fa1e156404722b195df5d878e2c9dfe09602be6a0830d2fe9ca996368fe
Transactions (2)
Coinbase80f62d4a5ce514…4b46e26ced4332
1 in β†’ 1 out8.4100 XPM109 B
AZagjC2G…9URube8X
af43484cef37f4…cbf9f82b1bce16
1 in β†’ 2 out4203.5117 XPM225 B
AVUk6kvB…CSJN4TqBAS4xUNny…7sgVvAGA
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.

7.318 Γ— 10⁹⁡(96-digit number)
73181432524123068053…15850492099343283201
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
7.318 Γ— 10⁹⁡(96-digit number)
73181432524123068053…15850492099343283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.463 Γ— 10⁹⁢(97-digit number)
14636286504824613610…31700984198686566401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.927 Γ— 10⁹⁢(97-digit number)
29272573009649227221…63401968397373132801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.854 Γ— 10⁹⁢(97-digit number)
58545146019298454443…26803936794746265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.170 Γ— 10⁹⁷(98-digit number)
11709029203859690888…53607873589492531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.341 Γ— 10⁹⁷(98-digit number)
23418058407719381777…07215747178985062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.683 Γ— 10⁹⁷(98-digit number)
46836116815438763554…14431494357970124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.367 Γ— 10⁹⁷(98-digit number)
93672233630877527109…28862988715940249601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.873 Γ— 10⁹⁸(99-digit number)
18734446726175505421…57725977431880499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.746 Γ— 10⁹⁸(99-digit number)
37468893452351010843…15451954863760998401
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:57,974,695 XPMΒ·at block #6,841,290 Β· updates every 60s
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