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Block #654,087

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2014, 11:32:30 PM Β· Difficulty 10.9552 Β· 6,147,184 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b5dd9c178e8d58296ebf1dc9932fb95ffbb5a473bca000bc97ac644b2d74842a
View on Chainz β†—

Height

#654,087

Difficulty

10.955169

Transactions

1

Size

208 B

Version

2

Bits

0af485f1

Nonce

163,819,837

Timestamp

7/29/2014, 11:32:30 PM

Confirmations

6,147,184

Merkle Root

8c2b4c0f63aec166c4d8dc03093233c3af8dba5a172227c135d16a0f8a8a8c0a
Transactions (1)
Coinbase8c2b4c0f63aec1…d16a0f8a8a8c0a
1 in β†’ 1 out8.3200 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.

3.961 Γ— 10⁹⁸(99-digit number)
39616207390760981131…51947394040372275200
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
3.961 Γ— 10⁹⁸(99-digit number)
39616207390760981131…51947394040372275199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.923 Γ— 10⁹⁸(99-digit number)
79232414781521962263…03894788080744550399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.584 Γ— 10⁹⁹(100-digit number)
15846482956304392452…07789576161489100799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.169 Γ— 10⁹⁹(100-digit number)
31692965912608784905…15579152322978201599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.338 Γ— 10⁹⁹(100-digit number)
63385931825217569810…31158304645956403199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.267 Γ— 10¹⁰⁰(101-digit number)
12677186365043513962…62316609291912806399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.535 Γ— 10¹⁰⁰(101-digit number)
25354372730087027924…24633218583825612799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.070 Γ— 10¹⁰⁰(101-digit number)
50708745460174055848…49266437167651225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.014 Γ— 10¹⁰¹(102-digit number)
10141749092034811169…98532874335302451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.028 Γ— 10¹⁰¹(102-digit number)
20283498184069622339…97065748670604902399
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 654087

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 b5dd9c178e8d58296ebf1dc9932fb95ffbb5a473bca000bc97ac644b2d74842a

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 #654,087 on Chainz β†—
Circulating Supply:57,654,232 XPMΒ·at block #6,801,270 Β· updates every 60s
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