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Block #123,473

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/19/2013, 2:11:42 AM Β· Difficulty 9.7637 Β· 6,692,789 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
392c3508334a10b1013af733db5f1fa625c961f43739685e628d8c6139fc5ded
View on Chainz β†—

Height

#123,473

Difficulty

9.763705

Transactions

1

Size

199 B

Version

2

Bits

09c3822e

Nonce

50,110

Timestamp

8/19/2013, 2:11:42 AM

Confirmations

6,692,789

Mined by

⛏️ P2SHAJYjKv6MiC978JMgPHsTyLZP4H8TXfzr5c

Merkle Root

a96f3fd80f379208150c154446a382b01841b8d2004b973898df11ec8871414e
Transactions (1)
Coinbasea96f3fd80f3792…df11ec8871414e
1 in β†’ 1 out10.4700 XPM109 B
AJYjKv6M…8TXfzr5c
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.

4.080 Γ— 10⁹⁴(95-digit number)
40807430207002690079…77554036190521114679
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
4.080 Γ— 10⁹⁴(95-digit number)
40807430207002690079…77554036190521114679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.161 Γ— 10⁹⁴(95-digit number)
81614860414005380159…55108072381042229359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁡(96-digit number)
16322972082801076031…10216144762084458719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.264 Γ— 10⁹⁡(96-digit number)
32645944165602152063…20432289524168917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.529 Γ— 10⁹⁡(96-digit number)
65291888331204304127…40864579048337834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁢(97-digit number)
13058377666240860825…81729158096675669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.611 Γ— 10⁹⁢(97-digit number)
26116755332481721651…63458316193351339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.223 Γ— 10⁹⁢(97-digit number)
52233510664963443302…26916632386702679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁷(98-digit number)
10446702132992688660…53833264773405358079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
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