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Block #155,227

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 4:41:37 AM Β· Difficulty 9.8656 Β· 6,657,473 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fac36740f604fdf9151a5e0906dcc52a73cecee8d6f6bc42cb47bfe510e878f7
View on Chainz β†—

Height

#155,227

Difficulty

9.865551

Transactions

1

Size

198 B

Version

2

Bits

09dd94ba

Nonce

19,562

Timestamp

9/8/2013, 4:41:37 AM

Confirmations

6,657,473

Merkle Root

3fa116bf54999915f39327817c5923693c40b30968ba2a9beffc2a89d2c6fbf0
Transactions (1)
Coinbase3fa116bf549999…fc2a89d2c6fbf0
1 in β†’ 1 out10.2600 XPM109 B
AaCW9UMs…1SP3NFNZ
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.

1.796 Γ— 10⁹²(93-digit number)
17965671775111356538…00057992065537495040
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
1.796 Γ— 10⁹²(93-digit number)
17965671775111356538…00057992065537495039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.593 Γ— 10⁹²(93-digit number)
35931343550222713076…00115984131074990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.186 Γ— 10⁹²(93-digit number)
71862687100445426153…00231968262149980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.437 Γ— 10⁹³(94-digit number)
14372537420089085230…00463936524299960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.874 Γ— 10⁹³(94-digit number)
28745074840178170461…00927873048599920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.749 Γ— 10⁹³(94-digit number)
57490149680356340923…01855746097199841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁴(95-digit number)
11498029936071268184…03711492194399682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.299 Γ— 10⁹⁴(95-digit number)
22996059872142536369…07422984388799365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.599 Γ— 10⁹⁴(95-digit number)
45992119744285072738…14845968777598730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.198 Γ— 10⁹⁴(95-digit number)
91984239488570145476…29691937555197460479
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 155227

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 fac36740f604fdf9151a5e0906dcc52a73cecee8d6f6bc42cb47bfe510e878f7

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 #155,227 on Chainz β†—
Circulating Supply:57,745,636 XPMΒ·at block #6,812,699 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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