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Block #215,972

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/18/2013, 11:24:37 AM Β· Difficulty 9.9253 Β· 6,611,389 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bc3d502b59d26f34f7c7fdfe1d7c7585c8208ca09141629e880dbb20d5d159fa
View on Chainz β†—

Height

#215,972

Difficulty

9.925292

Transactions

1

Size

207 B

Version

2

Bits

09ecdfe9

Nonce

50,333,081

Timestamp

10/18/2013, 11:24:37 AM

Confirmations

6,611,389

Merkle Root

e36c26085858f7171b50cef9914a0a2e98569d1a64850b3bab4d7951dd3adfc4
Transactions (1)
Coinbasee36c26085858f7…4d7951dd3adfc4
1 in β†’ 1 out10.1400 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.438 Γ— 10⁹⁢(97-digit number)
14382800987405551678…75437459671845913600
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
1.438 Γ— 10⁹⁢(97-digit number)
14382800987405551678…75437459671845913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.876 Γ— 10⁹⁢(97-digit number)
28765601974811103356…50874919343691827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.753 Γ— 10⁹⁢(97-digit number)
57531203949622206712…01749838687383654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.150 Γ— 10⁹⁷(98-digit number)
11506240789924441342…03499677374767308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.301 Γ— 10⁹⁷(98-digit number)
23012481579848882684…06999354749534617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.602 Γ— 10⁹⁷(98-digit number)
46024963159697765369…13998709499069235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.204 Γ— 10⁹⁷(98-digit number)
92049926319395530739…27997418998138470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.840 Γ— 10⁹⁸(99-digit number)
18409985263879106147…55994837996276940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.681 Γ— 10⁹⁸(99-digit number)
36819970527758212295…11989675992553881601
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 215972

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 bc3d502b59d26f34f7c7fdfe1d7c7585c8208ca09141629e880dbb20d5d159fa

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 #215,972 on Chainz β†—
Circulating Supply:57,862,987 XPMΒ·at block #6,827,360 Β· updates every 60s
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