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Block #1,479,070

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/1/2016, 6:37:26 PM Β· Difficulty 10.7121 Β· 5,364,249 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
829dbf1102306d10a691d4d1a676b7422069bec85aa12bde5eca1f736b4e3a7d
View on Chainz β†—

Difficulty

10.712148

Transactions

1

Size

200 B

Version

2

Bits

0ab64f57

Nonce

670,088,763

Timestamp

3/1/2016, 6:37:26 PM

Confirmations

5,364,249

Merkle Root

f6180128b39ba7c6310cee7f0d9c3a3e9d6354acf8b4414e6afd205a29489728
Transactions (1)
Coinbasef6180128b39ba7…fd205a29489728
1 in β†’ 1 out8.7000 XPM110 B
AHQnuU99…1VSfrdV1
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.

5.010 Γ— 10⁹⁡(96-digit number)
50104073142568499530…06134935696348736000
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
5.010 Γ— 10⁹⁡(96-digit number)
50104073142568499530…06134935696348736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.002 Γ— 10⁹⁢(97-digit number)
10020814628513699906…12269871392697472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.004 Γ— 10⁹⁢(97-digit number)
20041629257027399812…24539742785394944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.008 Γ— 10⁹⁢(97-digit number)
40083258514054799624…49079485570789888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.016 Γ— 10⁹⁢(97-digit number)
80166517028109599249…98158971141579776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.603 Γ— 10⁹⁷(98-digit number)
16033303405621919849…96317942283159552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.206 Γ— 10⁹⁷(98-digit number)
32066606811243839699…92635884566319104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.413 Γ— 10⁹⁷(98-digit number)
64133213622487679399…85271769132638208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.282 Γ— 10⁹⁸(99-digit number)
12826642724497535879…70543538265276416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.565 Γ— 10⁹⁸(99-digit number)
25653285448995071759…41087076530552832001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1479070

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 829dbf1102306d10a691d4d1a676b7422069bec85aa12bde5eca1f736b4e3a7d

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 #1,479,070 on Chainz β†—
Circulating Supply:57,990,911 XPMΒ·at block #6,843,318 Β· updates every 60s
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