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Block #15,456

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 7:33:49 PM Β· Difficulty 7.8524 Β· 6,794,938 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
78ffe189a5c1c26ff835f8b2b8a43f132059b0fa9f4ccbd1de66833d911c1c0d
View on Chainz β†—

Height

#15,456

Difficulty

7.852395

Transactions

1

Size

200 B

Version

2

Bits

07da368b

Nonce

37

Timestamp

7/11/2013, 7:33:49 PM

Confirmations

6,794,938

Merkle Root

7f8147ebc3423bbf96ca1fe7b6d16cb2139beb2c9863f89eb761c3e87a1aa5b7
Transactions (1)
Coinbase7f8147ebc3423b…61c3e87a1aa5b7
1 in β†’ 1 out16.2000 XPM108 B
ALtQiCyn…68VU6xPK
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.

1.487 Γ— 10⁹⁹(100-digit number)
14878846343757101512…95380902490881419050
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
1.487 Γ— 10⁹⁹(100-digit number)
14878846343757101512…95380902490881419051
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.975 Γ— 10⁹⁹(100-digit number)
29757692687514203025…90761804981762838101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.951 Γ— 10⁹⁹(100-digit number)
59515385375028406050…81523609963525676201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.190 Γ— 10¹⁰⁰(101-digit number)
11903077075005681210…63047219927051352401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.380 Γ— 10¹⁰⁰(101-digit number)
23806154150011362420…26094439854102704801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.761 Γ— 10¹⁰⁰(101-digit number)
47612308300022724840…52188879708205409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.522 Γ— 10¹⁰⁰(101-digit number)
95224616600045449680…04377759416410819201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 15456

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 78ffe189a5c1c26ff835f8b2b8a43f132059b0fa9f4ccbd1de66833d911c1c0d

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 #15,456 on Chainz β†—
Circulating Supply:57,727,229 XPMΒ·at block #6,810,393 Β· updates every 60s
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