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Block #1,035,317

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/27/2015, 8:34:09 PM Β· Difficulty 10.7439 Β· 5,804,813 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61eee3306389ed55d1eb68c35f1797d35877904cecac2c893d24c112413df42e
View on Chainz β†—

Height

#1,035,317

Difficulty

10.743925

Transactions

1

Size

242 B

Version

2

Bits

0abe71d7

Nonce

318,624,052

Timestamp

4/27/2015, 8:34:09 PM

Confirmations

5,804,813

Mined by

⛏️ P2SHAUV3ZXsawxZuaXubcanNHw2sUMP3xQCbyH

Merkle Root

cd04ade310bb8bdf5d26c087602f2f78ebecc0f47ebf9257527918b20b3f5630
Transactions (1)
Coinbasecd04ade310bb8b…7918b20b3f5630
1 in β†’ 2 out8.6500 XPM152 B
AUV3ZXsa…P3xQCbyHALPu3s2c…EJXLjVFh
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.

6.302 Γ— 10⁹⁴(95-digit number)
63022326087838900082…34806527699231930519
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
6.302 Γ— 10⁹⁴(95-digit number)
63022326087838900082…34806527699231930519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁡(96-digit number)
12604465217567780016…69613055398463861039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁡(96-digit number)
25208930435135560033…39226110796927722079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.041 Γ— 10⁹⁡(96-digit number)
50417860870271120066…78452221593855444159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁢(97-digit number)
10083572174054224013…56904443187710888319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁢(97-digit number)
20167144348108448026…13808886375421776639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.033 Γ— 10⁹⁢(97-digit number)
40334288696216896052…27617772750843553279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.066 Γ— 10⁹⁢(97-digit number)
80668577392433792105…55235545501687106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.613 Γ— 10⁹⁷(98-digit number)
16133715478486758421…10471091003374213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.226 Γ— 10⁹⁷(98-digit number)
32267430956973516842…20942182006748426239
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:57,965,354 XPMΒ·at block #6,840,129 Β· updates every 60s
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