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Block #1,612,596

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2016, 4:46:54 PM Β· Difficulty 10.6015 Β· 5,229,657 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
219b0ed2630a5a141c3e73c122c1988738873096e92999dd63c116d080fd8ede
View on Chainz β†—

Height

#1,612,596

Difficulty

10.601470

Transactions

1

Size

199 B

Version

2

Bits

0a99f9eb

Nonce

1,259,642,660

Timestamp

6/3/2016, 4:46:54 PM

Confirmations

5,229,657

Mined by

⛏️ P2SHAYwMZBdY8bf5f9mtT4Vuyotqbc1jYgcxDw

Merkle Root

48ce27df3f9a65325df461ad0189a6938794ae1296eb1a27ffb85d38e3d2ae1e
Transactions (1)
Coinbase48ce27df3f9a65…b85d38e3d2ae1e
1 in β†’ 1 out8.8800 XPM109 B
AYwMZBdY…1jYgcxDw
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.

6.898 Γ— 10⁹⁡(96-digit number)
68981522297647281920…50611573448948699839
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
6.898 Γ— 10⁹⁡(96-digit number)
68981522297647281920…50611573448948699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.379 Γ— 10⁹⁢(97-digit number)
13796304459529456384…01223146897897399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.759 Γ— 10⁹⁢(97-digit number)
27592608919058912768…02446293795794799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.518 Γ— 10⁹⁢(97-digit number)
55185217838117825536…04892587591589598719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.103 Γ— 10⁹⁷(98-digit number)
11037043567623565107…09785175183179197439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.207 Γ— 10⁹⁷(98-digit number)
22074087135247130214…19570350366358394879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.414 Γ— 10⁹⁷(98-digit number)
44148174270494260429…39140700732716789759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.829 Γ— 10⁹⁷(98-digit number)
88296348540988520858…78281401465433579519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.765 Γ— 10⁹⁸(99-digit number)
17659269708197704171…56562802930867159039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.531 Γ— 10⁹⁸(99-digit number)
35318539416395408343…13125605861734318079
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:57,982,421 XPMΒ·at block #6,842,252 Β· updates every 60s
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