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Block #217,988

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/19/2013, 4:21:07 PM Β· Difficulty 9.9294 Β· 6,598,126 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
24a4fa0b0341a58b9d43c0592b1786ada35c0dd948f18c6b89c01002f22b1b65
View on Chainz β†—

Height

#217,988

Difficulty

9.929430

Transactions

1

Size

207 B

Version

2

Bits

09edef1b

Nonce

83,887,789

Timestamp

10/19/2013, 4:21:07 PM

Confirmations

6,598,126

Merkle Root

061352affc999ae6a65c35da6cf5e4ce8440661816f914e3e9ae27c093e91ca8
Transactions (1)
Coinbase061352affc999a…ae27c093e91ca8
1 in β†’ 1 out10.1300 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.

6.972 Γ— 10⁹⁢(97-digit number)
69722715237127965036…05074257150192501760
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.972 Γ— 10⁹⁢(97-digit number)
69722715237127965036…05074257150192501759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.394 Γ— 10⁹⁷(98-digit number)
13944543047425593007…10148514300385003519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.788 Γ— 10⁹⁷(98-digit number)
27889086094851186014…20297028600770007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.577 Γ— 10⁹⁷(98-digit number)
55778172189702372028…40594057201540014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁸(99-digit number)
11155634437940474405…81188114403080028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.231 Γ— 10⁹⁸(99-digit number)
22311268875880948811…62376228806160056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.462 Γ— 10⁹⁸(99-digit number)
44622537751761897623…24752457612320112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.924 Γ— 10⁹⁸(99-digit number)
89245075503523795246…49504915224640225279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.784 Γ— 10⁹⁹(100-digit number)
17849015100704759049…99009830449280450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.569 Γ— 10⁹⁹(100-digit number)
35698030201409518098…98019660898560901119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 217988

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 24a4fa0b0341a58b9d43c0592b1786ada35c0dd948f18c6b89c01002f22b1b65

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 #217,988 on Chainz β†—
Circulating Supply:57,773,035 XPMΒ·at block #6,816,113 Β· updates every 60s
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