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Block #1,432,952

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/28/2016, 2:15:06 PM Β· Difficulty 10.7916 Β· 5,409,379 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97d4e97c5b150d56e618679c7aef53d25e729c4b4fb8629ce303ae2be7f23586
View on Chainz β†—

Height

#1,432,952

Difficulty

10.791646

Transactions

1

Size

201 B

Version

2

Bits

0acaa955

Nonce

440,538,041

Timestamp

1/28/2016, 2:15:06 PM

Confirmations

5,409,379

Mined by

⛏️ P2SHAeTQLp2QogRdCU2h8NR7LZGaKaYnpU9gfP

Merkle Root

f55d6156e3f1c5d1cb7ecbf1729d1df4615b8e547fa1e69984ab51ee79169180
Transactions (1)
Coinbasef55d6156e3f1c5…ab51ee79169180
1 in β†’ 1 out8.5700 XPM110 B
AeTQLp2Q…YnpU9gfP
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.

6.817 Γ— 10⁹⁢(97-digit number)
68176993860660757380…05969081943017149439
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
6.817 Γ— 10⁹⁢(97-digit number)
68176993860660757380…05969081943017149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.363 Γ— 10⁹⁷(98-digit number)
13635398772132151476…11938163886034298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.727 Γ— 10⁹⁷(98-digit number)
27270797544264302952…23876327772068597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.454 Γ— 10⁹⁷(98-digit number)
54541595088528605904…47752655544137195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.090 Γ— 10⁹⁸(99-digit number)
10908319017705721180…95505311088274391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.181 Γ— 10⁹⁸(99-digit number)
21816638035411442361…91010622176548782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.363 Γ— 10⁹⁸(99-digit number)
43633276070822884723…82021244353097564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.726 Γ— 10⁹⁸(99-digit number)
87266552141645769446…64042488706195128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.745 Γ— 10⁹⁹(100-digit number)
17453310428329153889…28084977412390256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.490 Γ— 10⁹⁹(100-digit number)
34906620856658307778…56169954824780513279
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:57,983,053 XPMΒ·at block #6,842,330 Β· updates every 60s
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