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Block #1,720,533

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2016, 11:44:04 PM Β· Difficulty 10.6750 Β· 5,110,977 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e1c6c23f3255b61fcd86cd824e4be718725382f2c51df7e6e598f1d00c1f012
View on Chainz β†—

Height

#1,720,533

Difficulty

10.675020

Transactions

1

Size

242 B

Version

2

Bits

0aacce14

Nonce

294,927,652

Timestamp

8/16/2016, 11:44:04 PM

Confirmations

5,110,977

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

ac5ca2dff286adf4ab37e85c4a44240c3f42708e163927f7c751920723cf6514
Transactions (1)
Coinbaseac5ca2dff286ad…51920723cf6514
1 in β†’ 2 out8.7600 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

8.373 Γ— 10⁹⁴(95-digit number)
83733624915345221272…75579051538358935999
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
8.373 Γ— 10⁹⁴(95-digit number)
83733624915345221272…75579051538358935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁡(96-digit number)
16746724983069044254…51158103076717871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.349 Γ— 10⁹⁡(96-digit number)
33493449966138088508…02316206153435743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.698 Γ— 10⁹⁡(96-digit number)
66986899932276177017…04632412306871487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁢(97-digit number)
13397379986455235403…09264824613742975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.679 Γ— 10⁹⁢(97-digit number)
26794759972910470807…18529649227485951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.358 Γ— 10⁹⁢(97-digit number)
53589519945820941614…37059298454971903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁷(98-digit number)
10717903989164188322…74118596909943807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁷(98-digit number)
21435807978328376645…48237193819887615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.287 Γ— 10⁹⁷(98-digit number)
42871615956656753291…96474387639775231999
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:57,896,169 XPMΒ·at block #6,831,509 Β· updates every 60s
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