XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #215,915

Block #215,915

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/18/2013, 10:29:30 AM Β· Difficulty 9.9253 Β· 6,584,637 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e16b718d75795535918f437dfee826dda843935bed3e43df282c8a47d3ff4dc1
View on Chainz β†—

Height

#215,915

Difficulty

9.925253

Transactions

1

Size

201 B

Version

2

Bits

09ecdd5f

Nonce

35,346

Timestamp

10/18/2013, 10:29:30 AM

Confirmations

6,584,637

Merkle Root

43472ae006231c3ea85a10646d8cd344bd8f9c3c3b970c90c76afd415a0c835d
Transactions (1)
Coinbase43472ae006231c…6afd415a0c835d
1 in β†’ 1 out10.1400 XPM110 B
AbuU1HhS…JPwsJEbB
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.

3.344 Γ— 10⁹⁢(97-digit number)
33446740144518379212…55412794188675491200
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
3.344 Γ— 10⁹⁢(97-digit number)
33446740144518379212…55412794188675491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.689 Γ— 10⁹⁢(97-digit number)
66893480289036758424…10825588377350982401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.337 Γ— 10⁹⁷(98-digit number)
13378696057807351684…21651176754701964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.675 Γ— 10⁹⁷(98-digit number)
26757392115614703369…43302353509403929601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.351 Γ— 10⁹⁷(98-digit number)
53514784231229406739…86604707018807859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.070 Γ— 10⁹⁸(99-digit number)
10702956846245881347…73209414037615718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.140 Γ— 10⁹⁸(99-digit number)
21405913692491762695…46418828075231436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.281 Γ— 10⁹⁸(99-digit number)
42811827384983525391…92837656150462873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.562 Γ— 10⁹⁸(99-digit number)
85623654769967050783…85675312300925747201
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.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
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 215915

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 e16b718d75795535918f437dfee826dda843935bed3e43df282c8a47d3ff4dc1

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 #215,915 on Chainz β†—
Circulating Supply:57,648,480 XPMΒ·at block #6,800,551 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