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Block #2,227,096

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2017, 6:36:13 PM Β· Difficulty 10.9480 Β· 4,615,885 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1398ceab4247b9924f7a8806e408a0c2beabd02a3cb85c8a64af0a2018b3f1e
View on Chainz β†—

Height

#2,227,096

Difficulty

10.948010

Transactions

1

Size

201 B

Version

2

Bits

0af2b0cd

Nonce

785,573,714

Timestamp

7/28/2017, 6:36:13 PM

Confirmations

4,615,885

Mined by

⛏️ P2SHANipT8PEQTqpDXy8HsdVU8Vs4CgNgTXjji

Merkle Root

c9f259fe752e4ce92a907ecac74e2b8ce794742079963756975d092bc2c71965
Transactions (1)
Coinbasec9f259fe752e4c…5d092bc2c71965
1 in β†’ 1 out8.3300 XPM110 B
ANipT8PE…gNgTXjji
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.

6.143 Γ— 10⁹⁢(97-digit number)
61438407658715525840…21460077717922616321
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
6.143 Γ— 10⁹⁢(97-digit number)
61438407658715525840…21460077717922616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.228 Γ— 10⁹⁷(98-digit number)
12287681531743105168…42920155435845232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.457 Γ— 10⁹⁷(98-digit number)
24575363063486210336…85840310871690465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.915 Γ— 10⁹⁷(98-digit number)
49150726126972420672…71680621743380930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.830 Γ— 10⁹⁷(98-digit number)
98301452253944841344…43361243486761861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.966 Γ— 10⁹⁸(99-digit number)
19660290450788968268…86722486973523722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.932 Γ— 10⁹⁸(99-digit number)
39320580901577936537…73444973947047444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.864 Γ— 10⁹⁸(99-digit number)
78641161803155873075…46889947894094888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.572 Γ— 10⁹⁹(100-digit number)
15728232360631174615…93779895788189777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.145 Γ— 10⁹⁹(100-digit number)
31456464721262349230…87559791576379555841
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:57,988,202 XPMΒ·at block #6,842,980 Β· updates every 60s
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