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Block #155,544

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 9:55:40 AM Β· Difficulty 9.8657 Β· 6,670,555 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65a020b9c8ba83f3742402c57ad4b60c465d3d31274628da1a2be80c54e465af
View on Chainz β†—

Height

#155,544

Difficulty

9.865702

Transactions

1

Size

200 B

Version

2

Bits

09dd9ea7

Nonce

251,189

Timestamp

9/8/2013, 9:55:40 AM

Confirmations

6,670,555

Merkle Root

208d2a35cb87d1fee849079ce8f40396f7da3b27501d28ff28c46d3d8bba55f2
Transactions (1)
Coinbase208d2a35cb87d1…c46d3d8bba55f2
1 in β†’ 1 out10.2600 XPM109 B
AVv2Uokw…Djqkjjws
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.

2.562 Γ— 10⁹⁢(97-digit number)
25620996430706914461…84262581803866792300
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
2.562 Γ— 10⁹⁢(97-digit number)
25620996430706914461…84262581803866792299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.124 Γ— 10⁹⁢(97-digit number)
51241992861413828922…68525163607733584599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.024 Γ— 10⁹⁷(98-digit number)
10248398572282765784…37050327215467169199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.049 Γ— 10⁹⁷(98-digit number)
20496797144565531568…74100654430934338399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.099 Γ— 10⁹⁷(98-digit number)
40993594289131063137…48201308861868676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.198 Γ— 10⁹⁷(98-digit number)
81987188578262126275…96402617723737353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.639 Γ— 10⁹⁸(99-digit number)
16397437715652425255…92805235447474707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.279 Γ— 10⁹⁸(99-digit number)
32794875431304850510…85610470894949414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.558 Γ— 10⁹⁸(99-digit number)
65589750862609701020…71220941789898828799
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 155544

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 65a020b9c8ba83f3742402c57ad4b60c465d3d31274628da1a2be80c54e465af

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 #155,544 on Chainz β†—
Circulating Supply:57,852,914 XPMΒ·at block #6,826,098 Β· updates every 60s
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