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Block #56,037

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 5:25:37 AM Β· Difficulty 8.9461 Β· 6,740,271 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a8962efc24d791c3b6f4009688300a50179d93cc2819659701902a53fe4cae4
View on Chainz β†—

Height

#56,037

Difficulty

8.946072

Transactions

1

Size

200 B

Version

2

Bits

08f231c0

Nonce

160

Timestamp

7/17/2013, 5:25:37 AM

Confirmations

6,740,271

Merkle Root

d7f0407f43f004f4f8caf44cbf825f12c0caee95d4ad49ca20f4f161fe71e5bf
Transactions (1)
Coinbased7f0407f43f004…f4f161fe71e5bf
1 in β†’ 1 out12.4800 XPM110 B
AW9WWG6Q…znay3MF1
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.

2.309 Γ— 10⁹⁡(96-digit number)
23095516353427752590…75256741065238529110
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.309 Γ— 10⁹⁡(96-digit number)
23095516353427752590…75256741065238529111
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.619 Γ— 10⁹⁡(96-digit number)
46191032706855505181…50513482130477058221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.238 Γ— 10⁹⁡(96-digit number)
92382065413711010363…01026964260954116441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.847 Γ— 10⁹⁢(97-digit number)
18476413082742202072…02053928521908232881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.695 Γ— 10⁹⁢(97-digit number)
36952826165484404145…04107857043816465761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.390 Γ— 10⁹⁢(97-digit number)
73905652330968808290…08215714087632931521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.478 Γ— 10⁹⁷(98-digit number)
14781130466193761658…16431428175265863041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.956 Γ— 10⁹⁷(98-digit number)
29562260932387523316…32862856350531726081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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 8
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 56037

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 1a8962efc24d791c3b6f4009688300a50179d93cc2819659701902a53fe4cae4

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 #56,037 on Chainz β†—
Circulating Supply:57,614,461 XPMΒ·at block #6,796,307 Β· updates every 60s
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