XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,371,748

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 5:09:55 PM Β· Difficulty 10.8110 Β· 5,468,514 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a704d5fbd65fddc8121a28f19c1384469ea2a2feb173cf7a6cd1afe346a057f4
View on Chainz β†—

Height

#1,371,748

Difficulty

10.810965

Transactions

1

Size

199 B

Version

2

Bits

0acf9b6b

Nonce

328,717,729

Timestamp

12/16/2015, 5:09:55 PM

Confirmations

5,468,514

Mined by

⛏️ P2SHAJR2oYwRKW9aSnK5RTWL7eiGfSBkAyaxbA

Merkle Root

30fde78b77f830f88aa30071ff2aa9ac1256c2eabd41a7ecec384713c179040c
Transactions (1)
Coinbase30fde78b77f830…384713c179040c
1 in β†’ 1 out8.5400 XPM109 B
AJR2oYwR…BkAyaxbA
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.

9.325 Γ— 10⁹⁴(95-digit number)
93253778141912072513…32549527849816111199
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
9.325 Γ— 10⁹⁴(95-digit number)
93253778141912072513…32549527849816111199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁡(96-digit number)
18650755628382414502…65099055699632222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.730 Γ— 10⁹⁡(96-digit number)
37301511256764829005…30198111399264444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.460 Γ— 10⁹⁡(96-digit number)
74603022513529658011…60396222798528889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁢(97-digit number)
14920604502705931602…20792445597057779199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁢(97-digit number)
29841209005411863204…41584891194115558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.968 Γ— 10⁹⁢(97-digit number)
59682418010823726408…83169782388231116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁷(98-digit number)
11936483602164745281…66339564776462233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁷(98-digit number)
23872967204329490563…32679129552924467199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁷(98-digit number)
47745934408658981127…65358259105848934399
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:57,966,409 XPMΒ·at block #6,840,261 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