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Block #2,138,961

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2017, 8:16:29 AM Β· Difficulty 10.8804 Β· 4,691,904 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a37be35e30f7607fb2fbebeb17cae8ac1ea1b1a6c35a1abd46280601ba6f9b56
View on Chainz β†—

Height

#2,138,961

Difficulty

10.880434

Transactions

1

Size

199 B

Version

2

Bits

0ae16418

Nonce

771,745,191

Timestamp

5/31/2017, 8:16:29 AM

Confirmations

4,691,904

Mined by

⛏️ P2SHALfzFf4MP8vFn9Gsa1Sg9GShgvLtxw6gJH

Merkle Root

3976f6c13dacfdc0b0552dcf6a82f7800d9ac196a56f02713ce1ee90ceeb6fe2
Transactions (1)
Coinbase3976f6c13dacfd…e1ee90ceeb6fe2
1 in β†’ 1 out8.4300 XPM109 B
ALfzFf4M…Ltxw6gJH
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.

6.202 Γ— 10⁹⁴(95-digit number)
62025027376325289453…43701187254315130879
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.202 Γ— 10⁹⁴(95-digit number)
62025027376325289453…43701187254315130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁡(96-digit number)
12405005475265057890…87402374508630261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.481 Γ— 10⁹⁡(96-digit number)
24810010950530115781…74804749017260523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.962 Γ— 10⁹⁡(96-digit number)
49620021901060231563…49609498034521047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.924 Γ— 10⁹⁡(96-digit number)
99240043802120463126…99218996069042094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.984 Γ— 10⁹⁢(97-digit number)
19848008760424092625…98437992138084188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.969 Γ— 10⁹⁢(97-digit number)
39696017520848185250…96875984276168376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.939 Γ— 10⁹⁢(97-digit number)
79392035041696370500…93751968552336752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.587 Γ— 10⁹⁷(98-digit number)
15878407008339274100…87503937104673505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.175 Γ— 10⁹⁷(98-digit number)
31756814016678548200…75007874209347010559
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,891,058 XPMΒ·at block #6,830,864 Β· updates every 60s
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