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Block #1,371,760

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2015, 5:21:41 PM Β· Difficulty 10.8109 Β· 5,466,455 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
820aec29755c26490bc74f924337e6f8dbc0969a56ee7851d1ee4efac8527fa0
View on Chainz β†—

Height

#1,371,760

Difficulty

10.810926

Transactions

1

Size

200 B

Version

2

Bits

0acf98dc

Nonce

56,980,359

Timestamp

12/16/2015, 5:21:41 PM

Confirmations

5,466,455

Mined by

⛏️ P2SHANBNVNkzpkpKjENFhfKTgkjZ6hzTuRDhui

Merkle Root

725149559c27841888db9726a63edb337b7a9b0d6135590b0cca532f7f89743a
Transactions (1)
Coinbase725149559c2784…ca532f7f89743a
1 in β†’ 1 out8.5400 XPM110 B
ANBNVNkz…zTuRDhui
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.

2.274 Γ— 10⁹⁡(96-digit number)
22743135353981046944…15770711196596392321
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
2.274 Γ— 10⁹⁡(96-digit number)
22743135353981046944…15770711196596392321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.548 Γ— 10⁹⁡(96-digit number)
45486270707962093889…31541422393192784641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.097 Γ— 10⁹⁡(96-digit number)
90972541415924187779…63082844786385569281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.819 Γ— 10⁹⁢(97-digit number)
18194508283184837555…26165689572771138561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.638 Γ— 10⁹⁢(97-digit number)
36389016566369675111…52331379145542277121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.277 Γ— 10⁹⁢(97-digit number)
72778033132739350223…04662758291084554241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.455 Γ— 10⁹⁷(98-digit number)
14555606626547870044…09325516582169108481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.911 Γ— 10⁹⁷(98-digit number)
29111213253095740089…18651033164338216961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.822 Γ— 10⁹⁷(98-digit number)
58222426506191480179…37302066328676433921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.164 Γ— 10⁹⁸(99-digit number)
11644485301238296035…74604132657352867841
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:57,949,994 XPMΒ·at block #6,838,214 Β· updates every 60s
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