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Block #157,646

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 6:43:55 PM Β· Difficulty 9.8692 Β· 6,669,032 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
271a097e02756c59baf3f7d4bca100e09968c9a027a2c7933493bc1bf11f0152
View on Chainz β†—

Height

#157,646

Difficulty

9.869236

Transactions

1

Size

204 B

Version

2

Bits

09de863d

Nonce

714,053

Timestamp

9/9/2013, 6:43:55 PM

Confirmations

6,669,032

Merkle Root

3e99f03a9e9a539f1f0b0e934c70341b70b757153de5c5b43fdf1c965eaee776
Transactions (1)
Coinbase3e99f03a9e9a53…df1c965eaee776
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.

8.911 Γ— 10⁹⁹(100-digit number)
89113300558711466255…16243413256445029790
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
8.911 Γ— 10⁹⁹(100-digit number)
89113300558711466255…16243413256445029791
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.782 Γ— 10¹⁰⁰(101-digit number)
17822660111742293251…32486826512890059581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.564 Γ— 10¹⁰⁰(101-digit number)
35645320223484586502…64973653025780119161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.129 Γ— 10¹⁰⁰(101-digit number)
71290640446969173004…29947306051560238321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.425 Γ— 10¹⁰¹(102-digit number)
14258128089393834600…59894612103120476641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.851 Γ— 10¹⁰¹(102-digit number)
28516256178787669201…19789224206240953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.703 Γ— 10¹⁰¹(102-digit number)
57032512357575338403…39578448412481906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.140 Γ— 10¹⁰²(103-digit number)
11406502471515067680…79156896824963813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.281 Γ— 10¹⁰²(103-digit number)
22813004943030135361…58313793649927626241
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 157646

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 271a097e02756c59baf3f7d4bca100e09968c9a027a2c7933493bc1bf11f0152

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 #157,646 on Chainz β†—
Circulating Supply:57,857,572 XPMΒ·at block #6,826,677 Β· updates every 60s
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