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Block #162,521

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2013, 9:07:49 AM Β· Difficulty 9.8612 Β· 6,633,002 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e86e3e54a51983a6b228f6a89df319c3e6b8dd4c9d142fd81a87d0de38e6714
View on Chainz β†—

Height

#162,521

Difficulty

9.861234

Transactions

1

Size

198 B

Version

2

Bits

09dc79d3

Nonce

309,799

Timestamp

9/13/2013, 9:07:49 AM

Confirmations

6,633,002

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

5d1a36e25845ed3de89c6b1084ad978b4511dd3a1fe78e0eb7eba3b28729d191
Transactions (1)
Coinbase5d1a36e25845ed…eba3b28729d191
1 in β†’ 1 out10.2700 XPM109 B
AX99MLNm…vtidqEwE
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.

1.069 Γ— 10⁹³(94-digit number)
10696525834389615062…89035318280784694549
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
1.069 Γ— 10⁹³(94-digit number)
10696525834389615062…89035318280784694549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.139 Γ— 10⁹³(94-digit number)
21393051668779230124…78070636561569389099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.278 Γ— 10⁹³(94-digit number)
42786103337558460248…56141273123138778199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.557 Γ— 10⁹³(94-digit number)
85572206675116920496…12282546246277556399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.711 Γ— 10⁹⁴(95-digit number)
17114441335023384099…24565092492555112799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.422 Γ— 10⁹⁴(95-digit number)
34228882670046768198…49130184985110225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.845 Γ— 10⁹⁴(95-digit number)
68457765340093536397…98260369970220451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.369 Γ— 10⁹⁡(96-digit number)
13691553068018707279…96520739940440902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.738 Γ— 10⁹⁡(96-digit number)
27383106136037414558…93041479880881804799
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:57,608,246 XPMΒ·at block #6,795,522 Β· updates every 60s
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