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Block #2,051,397

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 12:21:36 PM Β· Difficulty 10.7129 Β· 4,793,950 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6ac85c3ed0a2505b226978dcba527543f8a1e59a3ca1391dee47b77db8921afb
View on Chainz β†—

Height

#2,051,397

Difficulty

10.712947

Transactions

1

Size

200 B

Version

2

Bits

0ab683ad

Nonce

1,260,914,471

Timestamp

4/3/2017, 12:21:36 PM

Confirmations

4,793,950

Mined by

⛏️ P2SHAL54gZ8c9dic6S39eM24XDVcmwr47ycxEf

Merkle Root

85b3fa5f04b91a635fbaf6c44d6fdb722ee0943762d2d081c1988808ed9a7b8f
Transactions (1)
Coinbase85b3fa5f04b91a…988808ed9a7b8f
1 in β†’ 1 out8.7000 XPM110 B
AL54gZ8c…r47ycxEf
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.

2.105 Γ— 10⁹⁴(95-digit number)
21055115830504158913…61371083334646613999
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
2.105 Γ— 10⁹⁴(95-digit number)
21055115830504158913…61371083334646613999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.211 Γ— 10⁹⁴(95-digit number)
42110231661008317826…22742166669293227999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.422 Γ— 10⁹⁴(95-digit number)
84220463322016635653…45484333338586455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.684 Γ— 10⁹⁡(96-digit number)
16844092664403327130…90968666677172911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.368 Γ— 10⁹⁡(96-digit number)
33688185328806654261…81937333354345823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.737 Γ— 10⁹⁡(96-digit number)
67376370657613308522…63874666708691647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.347 Γ— 10⁹⁢(97-digit number)
13475274131522661704…27749333417383295999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.695 Γ— 10⁹⁢(97-digit number)
26950548263045323409…55498666834766591999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.390 Γ— 10⁹⁢(97-digit number)
53901096526090646818…10997333669533183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁷(98-digit number)
10780219305218129363…21994667339066367999
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:58,007,218 XPMΒ·at block #6,845,346 Β· updates every 60s
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