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Block #2,141,742

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2017, 11:38:18 AM Β· Difficulty 10.8732 Β· 4,701,395 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1c879a56fe68ce4a1098208e96e3797cf53e0aa30053ab47a53f59856bc1011
View on Chainz β†—

Height

#2,141,742

Difficulty

10.873200

Transactions

1

Size

199 B

Version

2

Bits

0adf8a0b

Nonce

467,967,250

Timestamp

6/2/2017, 11:38:18 AM

Confirmations

4,701,395

Mined by

⛏️ P2SHAUBeEaVHNtjK3Joc4p5E3CYvfwkiYcFu9w

Merkle Root

28eddbd92235b5502471d6e1e0cd535f78015b58d25402d81b53b707cbb3efa5
Transactions (1)
Coinbase28eddbd92235b5…53b707cbb3efa5
1 in β†’ 1 out8.4400 XPM109 B
AUBeEaVH…kiYcFu9w
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.

7.006 Γ— 10⁹⁡(96-digit number)
70064465125393596754…99746958059512892801
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
7.006 Γ— 10⁹⁡(96-digit number)
70064465125393596754…99746958059512892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.401 Γ— 10⁹⁢(97-digit number)
14012893025078719350…99493916119025785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.802 Γ— 10⁹⁢(97-digit number)
28025786050157438701…98987832238051571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.605 Γ— 10⁹⁢(97-digit number)
56051572100314877403…97975664476103142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.121 Γ— 10⁹⁷(98-digit number)
11210314420062975480…95951328952206284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.242 Γ— 10⁹⁷(98-digit number)
22420628840125950961…91902657904412569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.484 Γ— 10⁹⁷(98-digit number)
44841257680251901922…83805315808825139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.968 Γ— 10⁹⁷(98-digit number)
89682515360503803845…67610631617650278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.793 Γ— 10⁹⁸(99-digit number)
17936503072100760769…35221263235300556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.587 Γ— 10⁹⁸(99-digit number)
35873006144201521538…70442526470601113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.174 Γ— 10⁹⁸(99-digit number)
71746012288403043076…40885052941202227201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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
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