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Block #173,257

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 8:22:06 PM Β· Difficulty 9.8613 Β· 6,643,683 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a6e104aa9e9cf40d7e35100e0fc5f114a9822546e681c03fed6b49937c923c0e
View on Chainz β†—

Height

#173,257

Difficulty

9.861315

Transactions

1

Size

199 B

Version

2

Bits

09dc7f2a

Nonce

22,977

Timestamp

9/20/2013, 8:22:06 PM

Confirmations

6,643,683

Merkle Root

a1264e1f7c752babf42b69308c545ec2c07186ffde92ef12c5315859c366fe92
Transactions (1)
Coinbasea1264e1f7c752b…315859c366fe92
1 in β†’ 1 out10.2700 XPM109 B
AM1A9CZL…as4Lpogj
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.

6.171 Γ— 10⁹⁡(96-digit number)
61719089698244587825…48305482631906847360
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
6.171 Γ— 10⁹⁡(96-digit number)
61719089698244587825…48305482631906847361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.234 Γ— 10⁹⁢(97-digit number)
12343817939648917565…96610965263813694721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.468 Γ— 10⁹⁢(97-digit number)
24687635879297835130…93221930527627389441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.937 Γ— 10⁹⁢(97-digit number)
49375271758595670260…86443861055254778881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.875 Γ— 10⁹⁢(97-digit number)
98750543517191340520…72887722110509557761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.975 Γ— 10⁹⁷(98-digit number)
19750108703438268104…45775444221019115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.950 Γ— 10⁹⁷(98-digit number)
39500217406876536208…91550888442038231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.900 Γ— 10⁹⁷(98-digit number)
79000434813753072416…83101776884076462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.580 Γ— 10⁹⁸(99-digit number)
15800086962750614483…66203553768152924161
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 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 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 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 173257

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 a6e104aa9e9cf40d7e35100e0fc5f114a9822546e681c03fed6b49937c923c0e

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 #173,257 on Chainz β†—
Circulating Supply:57,779,562 XPMΒ·at block #6,816,939 Β· updates every 60s
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