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Home/Chain Registry/Block #1,263,156

Block #1,263,156

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/1/2015, 10:45:52 PM Β· Difficulty 10.8250 Β· 5,553,106 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c95e8a07dc598f15f20ab0062037c45870c8a151d4d277fa02a1108d2ea7550c
View on Chainz β†—

Difficulty

10.825002

Transactions

1

Size

200 B

Version

2

Bits

0ad3335a

Nonce

1,895,238,879

Timestamp

10/1/2015, 10:45:52 PM

Confirmations

5,553,106

Merkle Root

2d25f93adc09f3e1a61bd844578b6ee1645ec6a96fe1721b941ff1a57c914ec3
Transactions (1)
Coinbase2d25f93adc09f3…1ff1a57c914ec3
1 in β†’ 1 out8.5200 XPM109 B
APYvkKcb…nevAizob
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.

4.589 Γ— 10⁹⁢(97-digit number)
45893457615488891948…89780376064352893440
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
4.589 Γ— 10⁹⁢(97-digit number)
45893457615488891948…89780376064352893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.178 Γ— 10⁹⁢(97-digit number)
91786915230977783897…79560752128705786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.835 Γ— 10⁹⁷(98-digit number)
18357383046195556779…59121504257411573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.671 Γ— 10⁹⁷(98-digit number)
36714766092391113558…18243008514823147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.342 Γ— 10⁹⁷(98-digit number)
73429532184782227117…36486017029646295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.468 Γ— 10⁹⁸(99-digit number)
14685906436956445423…72972034059292590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.937 Γ— 10⁹⁸(99-digit number)
29371812873912890847…45944068118585180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.874 Γ— 10⁹⁸(99-digit number)
58743625747825781694…91888136237170360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.174 Γ— 10⁹⁹(100-digit number)
11748725149565156338…83776272474340720641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.349 Γ— 10⁹⁹(100-digit number)
23497450299130312677…67552544948681441281
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 1263156

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 c95e8a07dc598f15f20ab0062037c45870c8a151d4d277fa02a1108d2ea7550c

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 #1,263,156 on Chainz β†—
Circulating Supply:57,774,209 XPMΒ·at block #6,816,261 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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