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Block #2,275,985

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2017, 7:25:01 AM Β· Difficulty 10.9552 Β· 4,557,191 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e80c3271c2012f11aa7ba3c0089e2d2ec829ddac0e1bf65b9bbf31e1467d58fb
View on Chainz β†—

Height

#2,275,985

Difficulty

10.955193

Transactions

1

Size

200 B

Version

2

Bits

0af48787

Nonce

908,468,547

Timestamp

8/31/2017, 7:25:01 AM

Confirmations

4,557,191

Mined by

⛏️ P2SHAYaLP49Rw1Bg8ZuR8S5pF7UXGocGecqK6J

Merkle Root

29f113bca60a52d5911f89bf584cef577695deefb9dc919c3abb8915e8c432a7
Transactions (1)
Coinbase29f113bca60a52…bb8915e8c432a7
1 in β†’ 1 out8.3200 XPM110 B
AYaLP49R…cGecqK6J
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.

1.470 Γ— 10⁹⁴(95-digit number)
14705494532905369877…82884383348566036481
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
1.470 Γ— 10⁹⁴(95-digit number)
14705494532905369877…82884383348566036481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.941 Γ— 10⁹⁴(95-digit number)
29410989065810739754…65768766697132072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.882 Γ— 10⁹⁴(95-digit number)
58821978131621479508…31537533394264145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.176 Γ— 10⁹⁡(96-digit number)
11764395626324295901…63075066788528291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.352 Γ— 10⁹⁡(96-digit number)
23528791252648591803…26150133577056583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.705 Γ— 10⁹⁡(96-digit number)
47057582505297183607…52300267154113167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.411 Γ— 10⁹⁡(96-digit number)
94115165010594367214…04600534308226334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.882 Γ— 10⁹⁢(97-digit number)
18823033002118873442…09201068616452669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.764 Γ— 10⁹⁢(97-digit number)
37646066004237746885…18402137232905338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.529 Γ— 10⁹⁢(97-digit number)
75292132008475493771…36804274465810677761
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:57,909,590 XPMΒ·at block #6,833,175 Β· updates every 60s
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