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Block #1,613,707

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2016, 12:13:21 PM Β· Difficulty 10.5971 Β· 5,230,027 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
81c8a91c4116e4e75aadf6b2fbd055f5a971e88ee09136ab3579ab01653410a8
View on Chainz β†—

Height

#1,613,707

Difficulty

10.597062

Transactions

1

Size

200 B

Version

2

Bits

0a98d911

Nonce

1,707,239,773

Timestamp

6/4/2016, 12:13:21 PM

Confirmations

5,230,027

Mined by

⛏️ P2SHALMnBuSFchV83LzUBAAdpyxaazGoSm7XZo

Merkle Root

445a6f233c51ba0b9f0eedee8141199e1fdb188b1455860727046d34a1d15585
Transactions (1)
Coinbase445a6f233c51ba…046d34a1d15585
1 in β†’ 1 out8.8900 XPM109 B
ALMnBuSF…GoSm7XZo
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.

1.636 Γ— 10⁹⁷(98-digit number)
16364679116012741525…24567714311735336961
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
1.636 Γ— 10⁹⁷(98-digit number)
16364679116012741525…24567714311735336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.272 Γ— 10⁹⁷(98-digit number)
32729358232025483050…49135428623470673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.545 Γ— 10⁹⁷(98-digit number)
65458716464050966100…98270857246941347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.309 Γ— 10⁹⁸(99-digit number)
13091743292810193220…96541714493882695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.618 Γ— 10⁹⁸(99-digit number)
26183486585620386440…93083428987765391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.236 Γ— 10⁹⁸(99-digit number)
52366973171240772880…86166857975530782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.047 Γ— 10⁹⁹(100-digit number)
10473394634248154576…72333715951061565441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.094 Γ— 10⁹⁹(100-digit number)
20946789268496309152…44667431902123130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.189 Γ— 10⁹⁹(100-digit number)
41893578536992618304…89334863804246261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.378 Γ— 10⁹⁹(100-digit number)
83787157073985236608…78669727608492523521
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:57,994,239 XPMΒ·at block #6,843,733 Β· updates every 60s
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