XPM Prime Explorer symbol
XPMPrime Explorer

Block #155,317

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 6:03:51 AM Β· Difficulty 9.8658 Β· 6,659,721 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6b970c6ebdf10bd3b29a1673469bf238094b317996acc6e79ea1449c2142ecb9
View on Chainz β†—

Height

#155,317

Difficulty

9.865766

Transactions

1

Size

198 B

Version

2

Bits

09dda2db

Nonce

81,983

Timestamp

9/8/2013, 6:03:51 AM

Confirmations

6,659,721

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

8067addf472a51fccbc7c8bea5a4295d718312f292e27599074bf2e06b0d6faa
Transactions (1)
Coinbase8067addf472a51…4bf2e06b0d6faa
1 in β†’ 1 out10.2600 XPM109 B
ARwEjnek…XN12RHSr
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.

2.307 Γ— 10⁹³(94-digit number)
23074884604225949233…80335802519525934081
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.307 Γ— 10⁹³(94-digit number)
23074884604225949233…80335802519525934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.614 Γ— 10⁹³(94-digit number)
46149769208451898466…60671605039051868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.229 Γ— 10⁹³(94-digit number)
92299538416903796933…21343210078103736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.845 Γ— 10⁹⁴(95-digit number)
18459907683380759386…42686420156207472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.691 Γ— 10⁹⁴(95-digit number)
36919815366761518773…85372840312414945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.383 Γ— 10⁹⁴(95-digit number)
73839630733523037546…70745680624829890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.476 Γ— 10⁹⁡(96-digit number)
14767926146704607509…41491361249659781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.953 Γ— 10⁹⁡(96-digit number)
29535852293409215018…82982722499319562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.907 Γ— 10⁹⁡(96-digit number)
59071704586818430037…65965444998639124481
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,764,393 XPMΒ·at block #6,815,037 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