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Block #157,549

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 5:08:05 PM Β· Difficulty 9.8692 Β· 6,656,437 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
291675a7205fce2c3bd9d0f8afee563e03c7e50f0425458857e5e2baed09704d
View on Chainz β†—

Height

#157,549

Difficulty

9.869239

Transactions

1

Size

203 B

Version

2

Bits

09de8673

Nonce

569,880

Timestamp

9/9/2013, 5:08:05 PM

Confirmations

6,656,437

Merkle Root

e235e16bb58b005d7602e61a50452904646c0c5136282233313b65722fcc9296
Transactions (1)
Coinbasee235e16bb58b00…3b65722fcc9296
1 in β†’ 1 out10.2500 XPM112 B
AcLBm5Z9…S683d7c3
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.

9.165 Γ— 10⁹⁷(98-digit number)
91651924613526191785…52138356903595140000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
9.165 Γ— 10⁹⁷(98-digit number)
91651924613526191785…52138356903595140001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.833 Γ— 10⁹⁸(99-digit number)
18330384922705238357…04276713807190280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.666 Γ— 10⁹⁸(99-digit number)
36660769845410476714…08553427614380560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.332 Γ— 10⁹⁸(99-digit number)
73321539690820953428…17106855228761120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.466 Γ— 10⁹⁹(100-digit number)
14664307938164190685…34213710457522240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.932 Γ— 10⁹⁹(100-digit number)
29328615876328381371…68427420915044480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.865 Γ— 10⁹⁹(100-digit number)
58657231752656762742…36854841830088960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.173 Γ— 10¹⁰⁰(101-digit number)
11731446350531352548…73709683660177920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.346 Γ— 10¹⁰⁰(101-digit number)
23462892701062705097…47419367320355840001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 157549

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 291675a7205fce2c3bd9d0f8afee563e03c7e50f0425458857e5e2baed09704d

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 #157,549 on Chainz β†—
Circulating Supply:57,755,967 XPMΒ·at block #6,813,985 Β· updates every 60s
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