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Block #57,552

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 3:23:53 PM Β· Difficulty 8.9551 Β· 6,754,200 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43f7bb9958d1882a3b18f849056051d2c62f51deb38ad7a37c9ddee5ea7ad725
View on Chainz β†—

Height

#57,552

Difficulty

8.955083

Transactions

2

Size

3.02 KB

Version

2

Bits

08f48053

Nonce

250

Timestamp

7/17/2013, 3:23:53 PM

Confirmations

6,754,200

Merkle Root

d57a8016055a58b3213b08a5a96cf5c7f0b733f7677d10cadd943e7641da4240
Transactions (2)
Coinbase78e64a9d980e77…5d06df58a01343
1 in β†’ 1 out12.4800 XPM110 B
ALzWr4nr…9ZgbvGKE
64b5b46f42efcb…4ef7e622c52537
22 in β†’ 2 out795.2700 XPM2.83 KB
ARy4TpQ5…y7aPT5DqAbwh8C2p…3ybWVNut
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.

6.237 Γ— 10¹⁰¹(102-digit number)
62378657897071315239…64951360533758798300
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
6.237 Γ— 10¹⁰¹(102-digit number)
62378657897071315239…64951360533758798299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.247 Γ— 10¹⁰²(103-digit number)
12475731579414263047…29902721067517596599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.495 Γ— 10¹⁰²(103-digit number)
24951463158828526095…59805442135035193199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.990 Γ— 10¹⁰²(103-digit number)
49902926317657052191…19610884270070386399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.980 Γ— 10¹⁰²(103-digit number)
99805852635314104383…39221768540140772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.996 Γ— 10¹⁰³(104-digit number)
19961170527062820876…78443537080281545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.992 Γ— 10¹⁰³(104-digit number)
39922341054125641753…56887074160563091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.984 Γ— 10¹⁰³(104-digit number)
79844682108251283506…13774148321126182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.596 Γ— 10¹⁰⁴(105-digit number)
15968936421650256701…27548296642252364799
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 57552

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 43f7bb9958d1882a3b18f849056051d2c62f51deb38ad7a37c9ddee5ea7ad725

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 #57,552 on Chainz β†—
Circulating Supply:57,738,125 XPMΒ·at block #6,811,751 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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