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Block #152,405

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 7:40:56 AM Β· Difficulty 9.8622 Β· 6,672,194 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99667774e542332dc9fbc53ea77a99c129f272cca477b063f074244e8a71b3f9
View on Chainz β†—

Height

#152,405

Difficulty

9.862176

Transactions

1

Size

205 B

Version

2

Bits

09dcb78a

Nonce

16,084

Timestamp

9/6/2013, 7:40:56 AM

Confirmations

6,672,194

Merkle Root

4a7332a29aea9f74136602c977c6010bdfe82bc513c60033eb297ddf4183783e
Transactions (1)
Coinbase4a7332a29aea9f…297ddf4183783e
1 in β†’ 1 out10.2700 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.

1.106 Γ— 10¹⁰²(103-digit number)
11060693187212155689…75689942932846192420
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
1.106 Γ— 10¹⁰²(103-digit number)
11060693187212155689…75689942932846192419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.212 Γ— 10¹⁰²(103-digit number)
22121386374424311379…51379885865692384839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.424 Γ— 10¹⁰²(103-digit number)
44242772748848622758…02759771731384769679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.848 Γ— 10¹⁰²(103-digit number)
88485545497697245516…05519543462769539359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.769 Γ— 10¹⁰³(104-digit number)
17697109099539449103…11039086925539078719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.539 Γ— 10¹⁰³(104-digit number)
35394218199078898206…22078173851078157439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.078 Γ— 10¹⁰³(104-digit number)
70788436398157796413…44156347702156314879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.415 Γ— 10¹⁰⁴(105-digit number)
14157687279631559282…88312695404312629759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.831 Γ— 10¹⁰⁴(105-digit number)
28315374559263118565…76625390808625259519
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 152405

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 99667774e542332dc9fbc53ea77a99c129f272cca477b063f074244e8a71b3f9

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 #152,405 on Chainz β†—
Circulating Supply:57,840,861 XPMΒ·at block #6,824,598 Β· updates every 60s
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