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Home/Chain Registry/Block #114,973

Block #114,973

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2013, 11:57:10 AM Β· Difficulty 9.7414 Β· 6,697,761 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf52ba4294ebd08d0e88821f6591a0411291359bb55670ecdae784fb24147fb2
View on Chainz β†—

Height

#114,973

Difficulty

9.741393

Transactions

1

Size

200 B

Version

2

Bits

09bdcbe9

Nonce

257,742

Timestamp

8/13/2013, 11:57:10 AM

Confirmations

6,697,761

Merkle Root

30af0cc85d7f94d50fed329ef9572b7b8ba24b1477e50c53589ce15613dae0cc
Transactions (1)
Coinbase30af0cc85d7f94…9ce15613dae0cc
1 in β†’ 1 out10.5200 XPM109 B
AHxYTEQE…y5namzYw
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.

1.615 Γ— 10⁹⁢(97-digit number)
16152133525971509978…84000381452189279280
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
1.615 Γ— 10⁹⁢(97-digit number)
16152133525971509978…84000381452189279281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.230 Γ— 10⁹⁢(97-digit number)
32304267051943019956…68000762904378558561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.460 Γ— 10⁹⁢(97-digit number)
64608534103886039912…36001525808757117121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.292 Γ— 10⁹⁷(98-digit number)
12921706820777207982…72003051617514234241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.584 Γ— 10⁹⁷(98-digit number)
25843413641554415964…44006103235028468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.168 Γ— 10⁹⁷(98-digit number)
51686827283108831929…88012206470056936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.033 Γ— 10⁹⁸(99-digit number)
10337365456621766385…76024412940113873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.067 Γ— 10⁹⁸(99-digit number)
20674730913243532771…52048825880227747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.134 Γ— 10⁹⁸(99-digit number)
41349461826487065543…04097651760455495681
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 114973

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 bf52ba4294ebd08d0e88821f6591a0411291359bb55670ecdae784fb24147fb2

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 #114,973 on Chainz β†—
Circulating Supply:57,745,913 XPMΒ·at block #6,812,733 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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