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Block #1,725,721

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2016, 8:27:14 AM Β· Difficulty 10.6967 Β· 5,083,780 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a3d0557694e46a095278d7d763662a8ed38fa16610b25ce41b00d461638dace
View on Chainz β†—

Height

#1,725,721

Difficulty

10.696735

Transactions

1

Size

242 B

Version

2

Bits

0ab25d34

Nonce

753,065,464

Timestamp

8/20/2016, 8:27:14 AM

Confirmations

5,083,780

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

1fc4d427aa6687b4cfcc312c60fc2853619e1208b3136e73b82e1fca1ae0d509
Transactions (1)
Coinbase1fc4d427aa6687…2e1fca1ae0d509
1 in β†’ 2 out8.7300 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

5.537 Γ— 10⁹⁡(96-digit number)
55378054311782207339…55335370364025915119
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
5.537 Γ— 10⁹⁡(96-digit number)
55378054311782207339…55335370364025915119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁢(97-digit number)
11075610862356441467…10670740728051830239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.215 Γ— 10⁹⁢(97-digit number)
22151221724712882935…21341481456103660479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.430 Γ— 10⁹⁢(97-digit number)
44302443449425765871…42682962912207320959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.860 Γ— 10⁹⁢(97-digit number)
88604886898851531743…85365925824414641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁷(98-digit number)
17720977379770306348…70731851648829283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.544 Γ— 10⁹⁷(98-digit number)
35441954759540612697…41463703297658567679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.088 Γ— 10⁹⁷(98-digit number)
70883909519081225395…82927406595317135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.417 Γ— 10⁹⁸(99-digit number)
14176781903816245079…65854813190634270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.835 Γ— 10⁹⁸(99-digit number)
28353563807632490158…31709626381268541439
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:57,720,081 XPMΒ·at block #6,809,500 Β· updates every 60s
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