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Block #54,494

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 8:45:50 PM Β· Difficulty 8.9339 Β· 6,771,842 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
576f3a74efa834716758de9fef70ccf48e0db49f4632454e6427ef8e1344a12c
View on Chainz β†—

Height

#54,494

Difficulty

8.933878

Transactions

1

Size

202 B

Version

2

Bits

08ef12a3

Nonce

74

Timestamp

7/16/2013, 8:45:50 PM

Confirmations

6,771,842

Merkle Root

8c34a65ad32ad0a26d8bc0e41974eb9fa60faf5a7dd3c0135ebd6a6f937a5e3a
Transactions (1)
Coinbase8c34a65ad32ad0…bd6a6f937a5e3a
1 in β†’ 1 out12.5100 XPM110 B
AFw5xdbQ…Aq2dYHyv
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.

7.988 Γ— 10⁹⁹(100-digit number)
79886619011513771589…59239622946759258090
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
7.988 Γ— 10⁹⁹(100-digit number)
79886619011513771589…59239622946759258089
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.597 Γ— 10¹⁰⁰(101-digit number)
15977323802302754317…18479245893518516179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.195 Γ— 10¹⁰⁰(101-digit number)
31954647604605508635…36958491787037032359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.390 Γ— 10¹⁰⁰(101-digit number)
63909295209211017271…73916983574074064719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.278 Γ— 10¹⁰¹(102-digit number)
12781859041842203454…47833967148148129439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.556 Γ— 10¹⁰¹(102-digit number)
25563718083684406908…95667934296296258879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.112 Γ— 10¹⁰¹(102-digit number)
51127436167368813817…91335868592592517759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.022 Γ— 10¹⁰²(103-digit number)
10225487233473762763…82671737185185035519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.045 Γ— 10¹⁰²(103-digit number)
20450974466947525527…65343474370370071039
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 54494

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 576f3a74efa834716758de9fef70ccf48e0db49f4632454e6427ef8e1344a12c

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 #54,494 on Chainz β†—
Circulating Supply:57,854,830 XPMΒ·at block #6,826,335 Β· updates every 60s
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