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Block #625,164

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/9/2014, 11:57:05 AM Β· Difficulty 10.9591 Β· 6,206,375 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0681b8bfe5037a6c6287473a7e6a432f3143efc679724f30fdcfc14ac65cb833
View on Chainz β†—

Height

#625,164

Difficulty

10.959069

Transactions

1

Size

207 B

Version

2

Bits

0af5858b

Nonce

246,654,369

Timestamp

7/9/2014, 11:57:05 AM

Confirmations

6,206,375

Merkle Root

8c73ea1821f44a2def0594775f890aee9323f0612736f58151d86cb1717dc03c
Transactions (1)
Coinbase8c73ea1821f44a…d86cb1717dc03c
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.469 Γ— 10⁹⁷(98-digit number)
14696440401631482071…56064899331318097600
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
1.469 Γ— 10⁹⁷(98-digit number)
14696440401631482071…56064899331318097599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.939 Γ— 10⁹⁷(98-digit number)
29392880803262964143…12129798662636195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.878 Γ— 10⁹⁷(98-digit number)
58785761606525928287…24259597325272390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁸(99-digit number)
11757152321305185657…48519194650544780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.351 Γ— 10⁹⁸(99-digit number)
23514304642610371315…97038389301089561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.702 Γ— 10⁹⁸(99-digit number)
47028609285220742630…94076778602179123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.405 Γ— 10⁹⁸(99-digit number)
94057218570441485260…88153557204358246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁹(100-digit number)
18811443714088297052…76307114408716492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.762 Γ— 10⁹⁹(100-digit number)
37622887428176594104…52614228817432985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.524 Γ— 10⁹⁹(100-digit number)
75245774856353188208…05228457634865971199
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 625164

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 0681b8bfe5037a6c6287473a7e6a432f3143efc679724f30fdcfc14ac65cb833

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 #625,164 on Chainz β†—
Circulating Supply:57,896,402 XPMΒ·at block #6,831,538 Β· updates every 60s
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