XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,270,575

Block #1,270,575

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2015, 6:42:33 AM Β· Difficulty 10.8161 Β· 5,529,543 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2de33a14f0a469733f9fdc87433a22ed26e4020ad94e084e772ede68eaae7343
View on Chainz β†—

Difficulty

10.816072

Transactions

1

Size

208 B

Version

2

Bits

0ad0ea18

Nonce

1,173,740,141

Timestamp

10/7/2015, 6:42:33 AM

Confirmations

5,529,543

Merkle Root

b8fe29b78a9bd0a4398fe5ce6581c14cdcf3415d6d0002cf64ab930199a22367
Transactions (1)
Coinbaseb8fe29b78a9bd0…ab930199a22367
1 in β†’ 1 out8.5300 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.

2.470 Γ— 10⁹⁸(99-digit number)
24703010689178821695…69088158744414812160
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
2.470 Γ— 10⁹⁸(99-digit number)
24703010689178821695…69088158744414812159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.470 Γ— 10⁹⁸(99-digit number)
24703010689178821695…69088158744414812161
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
4.940 Γ— 10⁹⁸(99-digit number)
49406021378357643390…38176317488829624319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.940 Γ— 10⁹⁸(99-digit number)
49406021378357643390…38176317488829624321
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
9.881 Γ— 10⁹⁸(99-digit number)
98812042756715286781…76352634977659248639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.881 Γ— 10⁹⁸(99-digit number)
98812042756715286781…76352634977659248641
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
1.976 Γ— 10⁹⁹(100-digit number)
19762408551343057356…52705269955318497279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.976 Γ— 10⁹⁹(100-digit number)
19762408551343057356…52705269955318497281
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
3.952 Γ— 10⁹⁹(100-digit number)
39524817102686114712…05410539910636994559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.952 Γ— 10⁹⁹(100-digit number)
39524817102686114712…05410539910636994561
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 1270575

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 2de33a14f0a469733f9fdc87433a22ed26e4020ad94e084e772ede68eaae7343

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 #1,270,575 on Chainz β†—
Circulating Supply:57,645,005 XPMΒ·at block #6,800,117 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK