XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,736,031

Block #2,736,031

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/6/2018, 4:29:18 AM Β· Difficulty 11.6090 Β· 4,107,939 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09ff37be8d2f19524713bd863376c6401751abba03813d481b148b99c0f66bf3
View on Chainz β†—

Difficulty

11.609004

Transactions

1

Size

201 B

Version

2

Bits

0b9be7ab

Nonce

474,361,560

Timestamp

7/6/2018, 4:29:18 AM

Confirmations

4,107,939

Merkle Root

c062fbd8bc0b42ff55f739c9fad5def3e171dfeac8e0faef9b96ffd30c7d0ac2
Transactions (1)
Coinbasec062fbd8bc0b42…96ffd30c7d0ac2
1 in β†’ 1 out7.4100 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.498 Γ— 10⁹⁢(97-digit number)
14989274227788124397…50800641957952829440
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
1.498 Γ— 10⁹⁢(97-digit number)
14989274227788124397…50800641957952829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.997 Γ— 10⁹⁢(97-digit number)
29978548455576248795…01601283915905658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.995 Γ— 10⁹⁢(97-digit number)
59957096911152497590…03202567831811317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.199 Γ— 10⁹⁷(98-digit number)
11991419382230499518…06405135663622635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.398 Γ— 10⁹⁷(98-digit number)
23982838764460999036…12810271327245271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.796 Γ— 10⁹⁷(98-digit number)
47965677528921998072…25620542654490542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.593 Γ— 10⁹⁷(98-digit number)
95931355057843996145…51241085308981084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.918 Γ— 10⁹⁸(99-digit number)
19186271011568799229…02482170617962168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.837 Γ— 10⁹⁸(99-digit number)
38372542023137598458…04964341235924336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.674 Γ— 10⁹⁸(99-digit number)
76745084046275196916…09928682471848673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.534 Γ— 10⁹⁹(100-digit number)
15349016809255039383…19857364943697346561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2736031

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 09ff37be8d2f19524713bd863376c6401751abba03813d481b148b99c0f66bf3

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 #2,736,031 on Chainz β†—
Circulating Supply:57,996,138 XPMΒ·at block #6,843,969 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