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Block #217,169

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/19/2013, 4:45:08 AM Β· Difficulty 9.9276 Β· 6,585,385 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
19e4c14ca741b253c923a3278c855dcd3a1fa179d1d748290d26d8df9fe25540
View on Chainz β†—

Height

#217,169

Difficulty

9.927608

Transactions

1

Size

199 B

Version

2

Bits

09ed77b3

Nonce

1,355

Timestamp

10/19/2013, 4:45:08 AM

Confirmations

6,585,385

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

11ff7bfc838108d07cc97e21d25b15b486745b6357b3d8ecd42fb35f32cdc75b
Transactions (1)
Coinbase11ff7bfc838108…2fb35f32cdc75b
1 in β†’ 1 out10.1300 XPM109 B
AHPLSWVd…ZdicvSUu
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.

1.253 Γ— 10⁹⁴(95-digit number)
12532661954146576525…98211702869019142399
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
1.253 Γ— 10⁹⁴(95-digit number)
12532661954146576525…98211702869019142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.506 Γ— 10⁹⁴(95-digit number)
25065323908293153050…96423405738038284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.013 Γ— 10⁹⁴(95-digit number)
50130647816586306100…92846811476076569599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁡(96-digit number)
10026129563317261220…85693622952153139199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.005 Γ— 10⁹⁡(96-digit number)
20052259126634522440…71387245904306278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.010 Γ— 10⁹⁡(96-digit number)
40104518253269044880…42774491808612556799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.020 Γ— 10⁹⁡(96-digit number)
80209036506538089760…85548983617225113599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.604 Γ— 10⁹⁢(97-digit number)
16041807301307617952…71097967234450227199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.208 Γ— 10⁹⁢(97-digit number)
32083614602615235904…42195934468900454399
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
Circulating Supply:57,664,445 XPMΒ·at block #6,802,553 Β· updates every 60s
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