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Block #149,613

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 12:03:46 PM Β· Difficulty 9.8572 Β· 6,646,740 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83140f3f7c6914e01dde8a5d3e211c3899b49437e2985a2752b3f47e416b0f3b
View on Chainz β†—

Height

#149,613

Difficulty

9.857204

Transactions

2

Size

471 B

Version

2

Bits

09db71b6

Nonce

3,330

Timestamp

9/4/2013, 12:03:46 PM

Confirmations

6,646,740

Merkle Root

78c2ee82a42a7d5ba06a52b46f705529f01be23f7aaa80fec80b887296f7c122
Transactions (2)
Coinbase09f6fbc833b938…054136d9fa81a0
1 in β†’ 1 out10.2900 XPM109 B
AUEHTg8o…71mZzNns
d510bd98953e6d…3fe532957fcca6
2 in β†’ 1 out20.5900 XPM272 B
AJs27LEf…M76myr9t
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.

1.196 Γ— 10⁹⁡(96-digit number)
11969267009157109111…84899526422757035520
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
1.196 Γ— 10⁹⁡(96-digit number)
11969267009157109111…84899526422757035519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.393 Γ— 10⁹⁡(96-digit number)
23938534018314218222…69799052845514071039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.787 Γ— 10⁹⁡(96-digit number)
47877068036628436445…39598105691028142079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.575 Γ— 10⁹⁡(96-digit number)
95754136073256872891…79196211382056284159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.915 Γ— 10⁹⁢(97-digit number)
19150827214651374578…58392422764112568319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.830 Γ— 10⁹⁢(97-digit number)
38301654429302749156…16784845528225136639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.660 Γ— 10⁹⁢(97-digit number)
76603308858605498312…33569691056450273279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁷(98-digit number)
15320661771721099662…67139382112900546559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.064 Γ— 10⁹⁷(98-digit number)
30641323543442199325…34278764225801093119
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 149613

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 83140f3f7c6914e01dde8a5d3e211c3899b49437e2985a2752b3f47e416b0f3b

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 #149,613 on Chainz β†—
Circulating Supply:57,614,818 XPMΒ·at block #6,796,352 Β· updates every 60s
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