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Block #1,769,561

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/19/2016, 5:34:23 AM Β· Difficulty 10.7433 Β· 5,033,009 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68549b5eb74e0c974857525f588fc32e16357cdb71282e6360a5b08b6f1287ea
View on Chainz β†—

Height

#1,769,561

Difficulty

10.743315

Transactions

2

Size

54.18 KB

Version

2

Bits

0abe49df

Nonce

290,160,165

Timestamp

9/19/2016, 5:34:23 AM

Confirmations

5,033,009

Mined by

⛏️ P2SHAREAkMi8z5D2NGX4PM16atbK1duEyQ43R8

Merkle Root

b3920baa63c8a95599fa0647aeb740da167b709d02adf7b6f28e8e4e1b5a18c8
Transactions (2)
Coinbase43bef516f0b0b2…116260f4b0f0b0
1 in β†’ 1 out9.2300 XPM109 B
AREAkMi8…uEyQ43R8
5646c103e16766…1b1efdfa972274
373 in β†’ 2 out20000.0100 XPM53.98 KB
AekKDRSN…sGzApWSFAYKArr5V…V9VqiqCZ
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.

7.010 Γ— 10⁹⁴(95-digit number)
70105818977648307163…85118684363893887679
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
7.010 Γ— 10⁹⁴(95-digit number)
70105818977648307163…85118684363893887679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.402 Γ— 10⁹⁡(96-digit number)
14021163795529661432…70237368727787775359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.804 Γ— 10⁹⁡(96-digit number)
28042327591059322865…40474737455575550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.608 Γ— 10⁹⁡(96-digit number)
56084655182118645730…80949474911151101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.121 Γ— 10⁹⁢(97-digit number)
11216931036423729146…61898949822302202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.243 Γ— 10⁹⁢(97-digit number)
22433862072847458292…23797899644604405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.486 Γ— 10⁹⁢(97-digit number)
44867724145694916584…47595799289208811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.973 Γ— 10⁹⁢(97-digit number)
89735448291389833168…95191598578417623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.794 Γ— 10⁹⁷(98-digit number)
17947089658277966633…90383197156835246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.589 Γ— 10⁹⁷(98-digit number)
35894179316555933267…80766394313670492159
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:57,664,575 XPMΒ·at block #6,802,569 Β· updates every 60s
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