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Block #157,451

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 3:31:07 PM Β· Difficulty 9.8691 Β· 6,668,168 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
105405aedc3e6a45eb520d7ce92addbf7e27f59069d44f7056c4607c52a06f9b
View on Chainz β†—

Height

#157,451

Difficulty

9.869089

Transactions

1

Size

198 B

Version

2

Bits

09de7c9d

Nonce

97,026

Timestamp

9/9/2013, 3:31:07 PM

Confirmations

6,668,168

Merkle Root

83f3ebfaa122d5512e66d9af9603dba3381a1063fd5e9e8e29d5756077922bed
Transactions (1)
Coinbase83f3ebfaa122d5…d5756077922bed
1 in β†’ 1 out10.2500 XPM109 B
AV55pf9g…c4Jbvptx
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.

1.397 Γ— 10⁹³(94-digit number)
13974354347299689324…25358897971078577280
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
1.397 Γ— 10⁹³(94-digit number)
13974354347299689324…25358897971078577281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.794 Γ— 10⁹³(94-digit number)
27948708694599378649…50717795942157154561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.589 Γ— 10⁹³(94-digit number)
55897417389198757299…01435591884314309121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.117 Γ— 10⁹⁴(95-digit number)
11179483477839751459…02871183768628618241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.235 Γ— 10⁹⁴(95-digit number)
22358966955679502919…05742367537257236481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.471 Γ— 10⁹⁴(95-digit number)
44717933911359005839…11484735074514472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.943 Γ— 10⁹⁴(95-digit number)
89435867822718011679…22969470149028945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.788 Γ— 10⁹⁡(96-digit number)
17887173564543602335…45938940298057891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.577 Γ— 10⁹⁡(96-digit number)
35774347129087204671…91877880596115783681
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 157451

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 105405aedc3e6a45eb520d7ce92addbf7e27f59069d44f7056c4607c52a06f9b

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 #157,451 on Chainz β†—
Circulating Supply:57,849,054 XPMΒ·at block #6,825,618 Β· updates every 60s
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