XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #655,442

Block #655,442

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2014, 9:15:29 PM Β· Difficulty 10.9557 Β· 6,140,163 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b00e224e7a71d6cf45a9c90dfd838de364cc4fc759ab7ec6329ac8533d9ed70
View on Chainz β†—

Height

#655,442

Difficulty

10.955656

Transactions

1

Size

207 B

Version

2

Bits

0af4a5d7

Nonce

1,711,180,104

Timestamp

7/30/2014, 9:15:29 PM

Confirmations

6,140,163

Merkle Root

0bf85204074fd10c31543e8a4e3f93ea7fdb346b3fbfc409bcec23158fb2eab5
Transactions (1)
Coinbase0bf85204074fd1…ec23158fb2eab5
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.239 Γ— 10⁹⁷(98-digit number)
92399703175666453826…09010551446847892480
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
9.239 Γ— 10⁹⁷(98-digit number)
92399703175666453826…09010551446847892481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.847 Γ— 10⁹⁸(99-digit number)
18479940635133290765…18021102893695784961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.695 Γ— 10⁹⁸(99-digit number)
36959881270266581530…36042205787391569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.391 Γ— 10⁹⁸(99-digit number)
73919762540533163060…72084411574783139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.478 Γ— 10⁹⁹(100-digit number)
14783952508106632612…44168823149566279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.956 Γ— 10⁹⁹(100-digit number)
29567905016213265224…88337646299132559361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.913 Γ— 10⁹⁹(100-digit number)
59135810032426530448…76675292598265118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.182 Γ— 10¹⁰⁰(101-digit number)
11827162006485306089…53350585196530237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.365 Γ— 10¹⁰⁰(101-digit number)
23654324012970612179…06701170393060474881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.730 Γ— 10¹⁰⁰(101-digit number)
47308648025941224359…13402340786120949761
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 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 655442

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 2b00e224e7a71d6cf45a9c90dfd838de364cc4fc759ab7ec6329ac8533d9ed70

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #655,442 on Chainz β†—
Circulating Supply:57,608,904 XPMΒ·at block #6,795,604 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