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Block #61,673

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 2:43:45 PM Β· Difficulty 8.9739 Β· 6,747,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
039e9db64114069a7c0716fd1c57e51ece5cc3910c26f564002a5eb2e4a79416
View on Chainz β†—

Height

#61,673

Difficulty

8.973917

Transactions

1

Size

199 B

Version

2

Bits

08f952a4

Nonce

132

Timestamp

7/18/2013, 2:43:45 PM

Confirmations

6,747,481

Merkle Root

5cb6a1cf4ba6bc81aaee644498ac7620a2d310d7a6b42c65746e2a8ee11c8f9a
Transactions (1)
Coinbase5cb6a1cf4ba6bc…6e2a8ee11c8f9a
1 in β†’ 1 out12.4000 XPM110 B
AKsLKPc8…zkBgUqcr
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.

6.307 Γ— 10⁹¹(92-digit number)
63070356695176776720…76721432135164651720
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
6.307 Γ— 10⁹¹(92-digit number)
63070356695176776720…76721432135164651719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.261 Γ— 10⁹²(93-digit number)
12614071339035355344…53442864270329303439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.522 Γ— 10⁹²(93-digit number)
25228142678070710688…06885728540658606879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.045 Γ— 10⁹²(93-digit number)
50456285356141421376…13771457081317213759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.009 Γ— 10⁹³(94-digit number)
10091257071228284275…27542914162634427519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.018 Γ— 10⁹³(94-digit number)
20182514142456568550…55085828325268855039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.036 Γ— 10⁹³(94-digit number)
40365028284913137101…10171656650537710079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.073 Γ— 10⁹³(94-digit number)
80730056569826274202…20343313301075420159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.614 Γ— 10⁹⁴(95-digit number)
16146011313965254840…40686626602150840319
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 61673

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 039e9db64114069a7c0716fd1c57e51ece5cc3910c26f564002a5eb2e4a79416

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 #61,673 on Chainz β†—
Circulating Supply:57,717,292 XPMΒ·at block #6,809,153 Β· updates every 60s
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