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Block #2,177,493

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 2:30:44 PM Β· Difficulty 10.9230 Β· 4,660,608 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc899c088f602ad59456d87fcc93b434583e172de8e0dfa9abe6ea4415610534
View on Chainz β†—

Height

#2,177,493

Difficulty

10.923011

Transactions

2

Size

428 B

Version

2

Bits

0aec4a72

Nonce

2,077,622,313

Timestamp

6/25/2017, 2:30:44 PM

Confirmations

4,660,608

Mined by

⛏️ P2SHAbqWr5DBdmVSAeHWDEATF78qAuH6xNPHmd

Merkle Root

fde494035012f8877637f26f3c4ba0aa8707c9286b753ffc71cfb3eb8c68b9c4
Transactions (2)
Coinbase0cab865d0aee53…3ee89f1939dc57
1 in β†’ 1 out8.3800 XPM110 B
AbqWr5DB…H6xNPHmd
79b4bc6714790b…ec245a6e9e27ee
1 in β†’ 2 out1805.0199 XPM227 B
AN8szP8k…CGjYtVjhAQ1VvDr9…qeQe5WTQ
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.

1.925 Γ— 10⁹⁷(98-digit number)
19259525983970561823…56947489147688253439
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
1.925 Γ— 10⁹⁷(98-digit number)
19259525983970561823…56947489147688253439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.851 Γ— 10⁹⁷(98-digit number)
38519051967941123646…13894978295376506879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.703 Γ— 10⁹⁷(98-digit number)
77038103935882247292…27789956590753013759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁸(99-digit number)
15407620787176449458…55579913181506027519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.081 Γ— 10⁹⁸(99-digit number)
30815241574352898917…11159826363012055039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.163 Γ— 10⁹⁸(99-digit number)
61630483148705797834…22319652726024110079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁹(100-digit number)
12326096629741159566…44639305452048220159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.465 Γ— 10⁹⁹(100-digit number)
24652193259482319133…89278610904096440319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.930 Γ— 10⁹⁹(100-digit number)
49304386518964638267…78557221808192880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.860 Γ— 10⁹⁹(100-digit number)
98608773037929276534…57114443616385761279
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:57,949,161 XPMΒ·at block #6,838,100 Β· updates every 60s
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