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Block #2,170,788

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/21/2017, 5:17:32 PM Β· Difficulty 10.9038 Β· 4,671,511 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35873b952ecc98adc945424ce1217144943b4aa68025e542d396f91ff44112a8
View on Chainz β†—

Height

#2,170,788

Difficulty

10.903779

Transactions

1

Size

200 B

Version

2

Bits

0ae75e11

Nonce

1,716,425,050

Timestamp

6/21/2017, 5:17:32 PM

Confirmations

4,671,511

Mined by

⛏️ P2SHAV8PVLroLaDPr9vKCw6iyq7RmLc6TmhCk1

Merkle Root

fe58d0a26dff88ccb77d0545b7ec2e529c89e2d201f4153e81ffeab6df4da6a5
Transactions (1)
Coinbasefe58d0a26dff88…ffeab6df4da6a5
1 in β†’ 1 out8.4000 XPM109 B
AV8PVLro…c6TmhCk1
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.

1.532 Γ— 10⁹⁢(97-digit number)
15327711918461347617…57578008548391801599
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
1.532 Γ— 10⁹⁢(97-digit number)
15327711918461347617…57578008548391801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.065 Γ— 10⁹⁢(97-digit number)
30655423836922695235…15156017096783603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.131 Γ— 10⁹⁢(97-digit number)
61310847673845390471…30312034193567206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.226 Γ— 10⁹⁷(98-digit number)
12262169534769078094…60624068387134412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.452 Γ— 10⁹⁷(98-digit number)
24524339069538156188…21248136774268825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.904 Γ— 10⁹⁷(98-digit number)
49048678139076312376…42496273548537651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.809 Γ— 10⁹⁷(98-digit number)
98097356278152624753…84992547097075302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.961 Γ— 10⁹⁸(99-digit number)
19619471255630524950…69985094194150604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.923 Γ— 10⁹⁸(99-digit number)
39238942511261049901…39970188388301209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.847 Γ— 10⁹⁸(99-digit number)
78477885022522099802…79940376776602419199
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:57,982,796 XPMΒ·at block #6,842,298 Β· updates every 60s
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