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Block #2,177,871

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 7:23:38 PM Β· Difficulty 10.9243 Β· 4,658,679 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77094d05e10d4ef687bb4a5b7625e01256d71e8fb55e1d6469c3f5bce8e9371f
View on Chainz β†—

Height

#2,177,871

Difficulty

10.924296

Transactions

1

Size

200 B

Version

2

Bits

0aec9ead

Nonce

365,537,528

Timestamp

6/25/2017, 7:23:38 PM

Confirmations

4,658,679

Mined by

⛏️ P2SHARADHH6QNLXPAds1s1tyjqE9MpjnMFjdoH

Merkle Root

9b7929c0dcfae45b306458138118955ec07b7fa2d44be0660e9d52872e661b88
Transactions (1)
Coinbase9b7929c0dcfae4…9d52872e661b88
1 in β†’ 1 out8.3700 XPM110 B
ARADHH6Q…jnMFjdoH
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.

7.620 Γ— 10⁹⁴(95-digit number)
76206118655481651541…45818489101443437359
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
7.620 Γ— 10⁹⁴(95-digit number)
76206118655481651541…45818489101443437359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.524 Γ— 10⁹⁡(96-digit number)
15241223731096330308…91636978202886874719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.048 Γ— 10⁹⁡(96-digit number)
30482447462192660616…83273956405773749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.096 Γ— 10⁹⁡(96-digit number)
60964894924385321233…66547912811547498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.219 Γ— 10⁹⁢(97-digit number)
12192978984877064246…33095825623094997759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.438 Γ— 10⁹⁢(97-digit number)
24385957969754128493…66191651246189995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.877 Γ— 10⁹⁢(97-digit number)
48771915939508256986…32383302492379991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.754 Γ— 10⁹⁢(97-digit number)
97543831879016513973…64766604984759982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.950 Γ— 10⁹⁷(98-digit number)
19508766375803302794…29533209969519964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.901 Γ— 10⁹⁷(98-digit number)
39017532751606605589…59066419939039928319
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:57,936,664 XPMΒ·at block #6,836,549 Β· updates every 60s
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