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Block #154,554

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2013, 6:02:36 PM Β· Difficulty 9.8646 Β· 6,640,249 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
797414e75ae317f8f2f1dc0dd3c0e60e65ff584b8a2ce6a07a5a3382046a34cb
View on Chainz β†—

Height

#154,554

Difficulty

9.864639

Transactions

1

Size

205 B

Version

2

Bits

09dd58ff

Nonce

102,671

Timestamp

9/7/2013, 6:02:36 PM

Confirmations

6,640,249

Merkle Root

6dad7c552a32e347def3b57e9a64d599abcb3457de47e0a74fb15384de29b8a8
Transactions (1)
Coinbase6dad7c552a32e3…b15384de29b8a8
1 in β†’ 1 out10.2600 XPM112 B
AT5A2KL6…CT16n6i2
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.

8.506 Γ— 10¹⁰¹(102-digit number)
85067469284161020195…63592071202496725120
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
8.506 Γ— 10¹⁰¹(102-digit number)
85067469284161020195…63592071202496725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.701 Γ— 10¹⁰²(103-digit number)
17013493856832204039…27184142404993450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.402 Γ— 10¹⁰²(103-digit number)
34026987713664408078…54368284809986900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.805 Γ— 10¹⁰²(103-digit number)
68053975427328816156…08736569619973800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.361 Γ— 10¹⁰³(104-digit number)
13610795085465763231…17473139239947601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.722 Γ— 10¹⁰³(104-digit number)
27221590170931526462…34946278479895203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.444 Γ— 10¹⁰³(104-digit number)
54443180341863052924…69892556959790407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.088 Γ— 10¹⁰⁴(105-digit number)
10888636068372610584…39785113919580815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.177 Γ— 10¹⁰⁴(105-digit number)
21777272136745221169…79570227839161630719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.355 Γ— 10¹⁰⁴(105-digit number)
43554544273490442339…59140455678323261439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 154554

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 797414e75ae317f8f2f1dc0dd3c0e60e65ff584b8a2ce6a07a5a3382046a34cb

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 #154,554 on Chainz β†—
Circulating Supply:57,602,477 XPMΒ·at block #6,794,802 Β· updates every 60s
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