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Block #153,165

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 7:48:05 PM Β· Difficulty 9.8630 Β· 6,664,877 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
56e4156cdc8a8ed09ea7cde4e7857d20169bce7b614e1bbc4cbb428fff517118
View on Chainz β†—

Height

#153,165

Difficulty

9.863045

Transactions

1

Size

199 B

Version

2

Bits

09dcf07e

Nonce

311,193

Timestamp

9/6/2013, 7:48:05 PM

Confirmations

6,664,877

Merkle Root

b00e54a8c6c21c324c491a4e364b901d65bafd3b467223969e39d2b226e0103c
Transactions (1)
Coinbaseb00e54a8c6c21c…39d2b226e0103c
1 in β†’ 1 out10.2600 XPM109 B
AdcZsTmn…W8T9Ht6R
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.

8.908 Γ— 10⁹³(94-digit number)
89081136798898367169…67442357735363791280
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
8.908 Γ— 10⁹³(94-digit number)
89081136798898367169…67442357735363791279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.781 Γ— 10⁹⁴(95-digit number)
17816227359779673433…34884715470727582559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.563 Γ— 10⁹⁴(95-digit number)
35632454719559346867…69769430941455165119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.126 Γ— 10⁹⁴(95-digit number)
71264909439118693735…39538861882910330239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.425 Γ— 10⁹⁡(96-digit number)
14252981887823738747…79077723765820660479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.850 Γ— 10⁹⁡(96-digit number)
28505963775647477494…58155447531641320959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.701 Γ— 10⁹⁡(96-digit number)
57011927551294954988…16310895063282641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁢(97-digit number)
11402385510258990997…32621790126565283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.280 Γ— 10⁹⁢(97-digit number)
22804771020517981995…65243580253130567679
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 153165

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 56e4156cdc8a8ed09ea7cde4e7857d20169bce7b614e1bbc4cbb428fff517118

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 #153,165 on Chainz β†—
Circulating Supply:57,788,406 XPMΒ·at block #6,818,041 Β· updates every 60s
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