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Block #156,211

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 7:41:35 PM Β· Difficulty 9.8678 Β· 6,658,886 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
578a4d1a835e5b4a935a588c1e5c51be085546dc890a35348ea9f5c4869503b9
View on Chainz β†—

Height

#156,211

Difficulty

9.867829

Transactions

1

Size

200 B

Version

2

Bits

09de2a11

Nonce

198,947

Timestamp

9/8/2013, 7:41:35 PM

Confirmations

6,658,886

Merkle Root

f923e6e40968f9dedca290c27f9ca0238d8eed6ca0c2bab08516b07a784f6925
Transactions (1)
Coinbasef923e6e40968f9…16b07a784f6925
1 in β†’ 1 out10.2500 XPM109 B
AJYjKv6M…8TXfzr5c
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.

2.925 Γ— 10⁹⁢(97-digit number)
29256025765133713958…91186302800794072640
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
2.925 Γ— 10⁹⁢(97-digit number)
29256025765133713958…91186302800794072639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.851 Γ— 10⁹⁢(97-digit number)
58512051530267427916…82372605601588145279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁷(98-digit number)
11702410306053485583…64745211203176290559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.340 Γ— 10⁹⁷(98-digit number)
23404820612106971166…29490422406352581119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.680 Γ— 10⁹⁷(98-digit number)
46809641224213942333…58980844812705162239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.361 Γ— 10⁹⁷(98-digit number)
93619282448427884667…17961689625410324479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.872 Γ— 10⁹⁸(99-digit number)
18723856489685576933…35923379250820648959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.744 Γ— 10⁹⁸(99-digit number)
37447712979371153866…71846758501641297919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.489 Γ— 10⁹⁸(99-digit number)
74895425958742307733…43693517003282595839
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 156211

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 578a4d1a835e5b4a935a588c1e5c51be085546dc890a35348ea9f5c4869503b9

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 #156,211 on Chainz β†—
Circulating Supply:57,764,864 XPMΒ·at block #6,815,096 Β· updates every 60s
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