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Block #2,177,336

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 12:30:21 PM Β· Difficulty 10.9224 Β· 4,667,551 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
355697214beddf52e395bb3e037509d7c11f6ebb60e4420b83b08e364e911bbc
View on Chainz β†—

Height

#2,177,336

Difficulty

10.922430

Transactions

1

Size

200 B

Version

2

Bits

0aec245b

Nonce

1,121,368,873

Timestamp

6/25/2017, 12:30:21 PM

Confirmations

4,667,551

Mined by

⛏️ P2SHAVdWrgYB6nqd396d3oq6wykNvUJ4gBoDgW

Merkle Root

70e506c9e65c870159a750534401212242daf6ebfb52dc76707034f969f46195
Transactions (1)
Coinbase70e506c9e65c87…7034f969f46195
1 in β†’ 1 out8.3700 XPM110 B
AVdWrgYB…J4gBoDgW
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.

1.145 Γ— 10⁹⁴(95-digit number)
11459810935342908444…13449866296590045599
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
1.145 Γ— 10⁹⁴(95-digit number)
11459810935342908444…13449866296590045599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁴(95-digit number)
22919621870685816888…26899732593180091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.583 Γ— 10⁹⁴(95-digit number)
45839243741371633777…53799465186360182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.167 Γ— 10⁹⁴(95-digit number)
91678487482743267554…07598930372720364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁡(96-digit number)
18335697496548653510…15197860745440729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.667 Γ— 10⁹⁡(96-digit number)
36671394993097307021…30395721490881459199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.334 Γ— 10⁹⁡(96-digit number)
73342789986194614043…60791442981762918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁢(97-digit number)
14668557997238922808…21582885963525836799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.933 Γ— 10⁹⁢(97-digit number)
29337115994477845617…43165771927051673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.867 Γ— 10⁹⁢(97-digit number)
58674231988955691234…86331543854103347199
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:58,003,510 XPMΒ·at block #6,844,886 Β· updates every 60s
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