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Home/Chain Registry/Block #1,257,629

Block #1,257,629

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/28/2015, 11:01:16 AM Β· Difficulty 10.8065 Β· 5,556,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7394db6ed9d317e83e06d8f4d5ef96e0040e3434ec9d536c8bd3cb5be8f123a3
View on Chainz β†—

Difficulty

10.806479

Transactions

1

Size

201 B

Version

2

Bits

0ace756c

Nonce

867,169,034

Timestamp

9/28/2015, 11:01:16 AM

Confirmations

5,556,856

Merkle Root

67e22f08bc960eff1eec9e4f9499e7e8cd5023f432f2b5e1458c3a2bc92f80b6
Transactions (1)
Coinbase67e22f08bc960e…8c3a2bc92f80b6
1 in β†’ 1 out8.5500 XPM110 B
APWByAFE…obuWvENK
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.

9.261 Γ— 10⁹⁡(96-digit number)
92611983748573285305…40858604456381849600
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
9.261 Γ— 10⁹⁡(96-digit number)
92611983748573285305…40858604456381849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.852 Γ— 10⁹⁢(97-digit number)
18522396749714657061…81717208912763699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.704 Γ— 10⁹⁢(97-digit number)
37044793499429314122…63434417825527398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.408 Γ— 10⁹⁢(97-digit number)
74089586998858628244…26868835651054796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.481 Γ— 10⁹⁷(98-digit number)
14817917399771725648…53737671302109593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.963 Γ— 10⁹⁷(98-digit number)
29635834799543451297…07475342604219187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.927 Γ— 10⁹⁷(98-digit number)
59271669599086902595…14950685208438374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.185 Γ— 10⁹⁸(99-digit number)
11854333919817380519…29901370416876748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.370 Γ— 10⁹⁸(99-digit number)
23708667839634761038…59802740833753497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.741 Γ— 10⁹⁸(99-digit number)
47417335679269522076…19605481667506995201
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 1257629

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 7394db6ed9d317e83e06d8f4d5ef96e0040e3434ec9d536c8bd3cb5be8f123a3

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 #1,257,629 on Chainz β†—
Circulating Supply:57,759,948 XPMΒ·at block #6,814,484 Β· updates every 60s
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