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Home/Chain Registry/Block #1,252,452

Block #1,252,452

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/25/2015, 6:05:21 AM Β· Difficulty 10.7835 Β· 5,573,855 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7711ad82d3dcc45ed686dfef32bc050e81d2d1106b8a3b9b92b225e635ff43ec
View on Chainz β†—

Difficulty

10.783496

Transactions

1

Size

207 B

Version

2

Bits

0ac89332

Nonce

2,248,679,090

Timestamp

9/25/2015, 6:05:21 AM

Confirmations

5,573,855

Merkle Root

fb5821e1b6b01f23de05ca4cd34d5b3eeb01822ba294b565dc4594495e58ef22
Transactions (1)
Coinbasefb5821e1b6b01f…4594495e58ef22
1 in β†’ 1 out8.5900 XPM116 B
AJCEY9yy…tg97E6zm
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.

9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593920
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.803 Γ— 10⁹⁸(99-digit number)
18033115782302302209…66274098862241187839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.803 Γ— 10⁹⁸(99-digit number)
18033115782302302209…66274098862241187841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.606 Γ— 10⁹⁸(99-digit number)
36066231564604604418…32548197724482375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.606 Γ— 10⁹⁸(99-digit number)
36066231564604604418…32548197724482375681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
7.213 Γ— 10⁹⁸(99-digit number)
72132463129209208837…65096395448964751359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.213 Γ— 10⁹⁸(99-digit number)
72132463129209208837…65096395448964751361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.442 Γ— 10⁹⁹(100-digit number)
14426492625841841767…30192790897929502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.442 Γ— 10⁹⁹(100-digit number)
14426492625841841767…30192790897929502721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 1252452

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 7711ad82d3dcc45ed686dfef32bc050e81d2d1106b8a3b9b92b225e635ff43ec

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 #1,252,452 on Chainz β†—
Circulating Supply:57,854,595 XPMΒ·at block #6,826,306 Β· updates every 60s
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