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Block #217,857

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/19/2013, 2:41:47 PM Β· Difficulty 9.9290 Β· 6,606,726 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61c70a288a83000fa35e4e4ad128ff6bbe8766aceb551cab42c0f1ecb8107e49
View on Chainz β†—

Height

#217,857

Difficulty

9.928961

Transactions

1

Size

206 B

Version

2

Bits

09edd062

Nonce

172,171

Timestamp

10/19/2013, 2:41:47 PM

Confirmations

6,606,726

Merkle Root

b4103d7d82dc52a6ab01cc4a2cea6ec48ccd442b5fc13825841986d26281ef8f
Transactions (1)
Coinbaseb4103d7d82dc52…1986d26281ef8f
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.

7.398 Γ— 10⁹³(94-digit number)
73989593732537424394…94451690767514431680
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
7.398 Γ— 10⁹³(94-digit number)
73989593732537424394…94451690767514431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁴(95-digit number)
14797918746507484878…88903381535028863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.959 Γ— 10⁹⁴(95-digit number)
29595837493014969757…77806763070057726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.919 Γ— 10⁹⁴(95-digit number)
59191674986029939515…55613526140115453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁡(96-digit number)
11838334997205987903…11227052280230906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.367 Γ— 10⁹⁡(96-digit number)
23676669994411975806…22454104560461813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.735 Γ— 10⁹⁡(96-digit number)
47353339988823951612…44908209120923627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.470 Γ— 10⁹⁡(96-digit number)
94706679977647903225…89816418241847255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.894 Γ— 10⁹⁢(97-digit number)
18941335995529580645…79632836483694510079
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 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
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 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 217857

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 61c70a288a83000fa35e4e4ad128ff6bbe8766aceb551cab42c0f1ecb8107e49

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 #217,857 on Chainz β†—
Circulating Supply:57,840,731 XPMΒ·at block #6,824,582 Β· updates every 60s
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