XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,221,698

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2015, 12:22:20 PM Β· Difficulty 10.7406 Β· 5,584,983 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
62f0be6af2469523a8e28a3f42c36d92c787adac94aa36f3adae9c305367cf2c
View on Chainz β†—

Height

#1,221,698

Difficulty

10.740601

Transactions

1

Size

200 B

Version

2

Bits

0abd9801

Nonce

477,807,406

Timestamp

9/4/2015, 12:22:20 PM

Confirmations

5,584,983

Mined by

⛏️ P2SHALUDpg5V52AXUZHeFvEjtz492UnHDRNGFJ

Merkle Root

6a6254bb6a013a2c6ba841af35cf9eb8df1035739f8143344090fd9b23ba6f38
Transactions (1)
Coinbase6a6254bb6a013a…90fd9b23ba6f38
1 in β†’ 1 out8.6500 XPM109 B
ALUDpg5V…nHDRNGFJ
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.

6.635 Γ— 10⁹⁢(97-digit number)
66358900803715516189…09687065558017940479
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
6.635 Γ— 10⁹⁢(97-digit number)
66358900803715516189…09687065558017940479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.327 Γ— 10⁹⁷(98-digit number)
13271780160743103237…19374131116035880959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.654 Γ— 10⁹⁷(98-digit number)
26543560321486206475…38748262232071761919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.308 Γ— 10⁹⁷(98-digit number)
53087120642972412951…77496524464143523839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.061 Γ— 10⁹⁸(99-digit number)
10617424128594482590…54993048928287047679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.123 Γ— 10⁹⁸(99-digit number)
21234848257188965180…09986097856574095359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.246 Γ— 10⁹⁸(99-digit number)
42469696514377930361…19972195713148190719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.493 Γ— 10⁹⁸(99-digit number)
84939393028755860722…39944391426296381439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.698 Γ— 10⁹⁹(100-digit number)
16987878605751172144…79888782852592762879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.397 Γ— 10⁹⁹(100-digit number)
33975757211502344289…59777565705185525759
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:57,697,541 XPMΒ·at block #6,806,680 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.
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