XPM Prime Explorer symbol
XPMPrime Explorer

Block #159,672

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 7:44:22 AM Β· Difficulty 9.8642 Β· 6,636,018 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4da9265fd07f486e9022ba6661ad03448ce4de9f2bb030afebebd827690963ad
View on Chainz β†—

Height

#159,672

Difficulty

9.864166

Transactions

1

Size

200 B

Version

2

Bits

09dd3a01

Nonce

6,817

Timestamp

9/11/2013, 7:44:22 AM

Confirmations

6,636,018

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

138d3fdb3aac2fef6755571158b4d9f41d95a03aaa86c2aadab83d5ad11d0a8c
Transactions (1)
Coinbase138d3fdb3aac2f…b83d5ad11d0a8c
1 in β†’ 1 out10.2600 XPM109 B
AJQ7bqzh…oY2ANRaW
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.

7.912 Γ— 10⁹⁷(98-digit number)
79121734538050477413…03713505833830291841
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
7.912 Γ— 10⁹⁷(98-digit number)
79121734538050477413…03713505833830291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.582 Γ— 10⁹⁸(99-digit number)
15824346907610095482…07427011667660583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.164 Γ— 10⁹⁸(99-digit number)
31648693815220190965…14854023335321167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.329 Γ— 10⁹⁸(99-digit number)
63297387630440381931…29708046670642334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.265 Γ— 10⁹⁹(100-digit number)
12659477526088076386…59416093341284669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.531 Γ— 10⁹⁹(100-digit number)
25318955052176152772…18832186682569338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.063 Γ— 10⁹⁹(100-digit number)
50637910104352305544…37664373365138677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.012 Γ— 10¹⁰⁰(101-digit number)
10127582020870461108…75328746730277355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.025 Γ— 10¹⁰⁰(101-digit number)
20255164041740922217…50657493460554711041
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:57,609,590 XPMΒ·at block #6,795,689 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