XPM Prime Explorer symbol
XPMPrime Explorer

Block #220,969

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2013, 7:52:32 AM Β· Difficulty 9.9376 Β· 6,623,972 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b9864457aa5062e253b9b91688436a3494d1085b91821fd93e7556543fabbf24
View on Chainz β†—

Height

#220,969

Difficulty

9.937571

Transactions

1

Size

198 B

Version

2

Bits

09f004a3

Nonce

51,829

Timestamp

10/21/2013, 7:52:32 AM

Confirmations

6,623,972

Mined by

⛏️ P2SHAQrMiFdw8DiHRbNsXgoebKaZbsRYqjzM7k

Merkle Root

393f85290e305e82bf748ec21060220cd1f3726acac8cad1805552e5f7dce049
Transactions (1)
Coinbase393f85290e305e…5552e5f7dce049
1 in β†’ 1 out10.1100 XPM109 B
AQrMiFdw…RYqjzM7k
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.

2.129 Γ— 10⁹³(94-digit number)
21292968875447617353…69152938166017199789
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
2.129 Γ— 10⁹³(94-digit number)
21292968875447617353…69152938166017199789
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.258 Γ— 10⁹³(94-digit number)
42585937750895234706…38305876332034399579
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.517 Γ— 10⁹³(94-digit number)
85171875501790469413…76611752664068799159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.703 Γ— 10⁹⁴(95-digit number)
17034375100358093882…53223505328137598319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.406 Γ— 10⁹⁴(95-digit number)
34068750200716187765…06447010656275196639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.813 Γ— 10⁹⁴(95-digit number)
68137500401432375531…12894021312550393279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.362 Γ— 10⁹⁡(96-digit number)
13627500080286475106…25788042625100786559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.725 Γ— 10⁹⁡(96-digit number)
27255000160572950212…51576085250201573119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.451 Γ— 10⁹⁡(96-digit number)
54510000321145900424…03152170500403146239
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:58,003,947 XPMΒ·at block #6,844,940 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy