XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #429,071

Block #429,071

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2014, 1:01:21 PM Β· Difficulty 10.3456 Β· 6,371,251 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
76c8046adee448fd9be923f4d3f676e0a75a57999581f20170fe28084a2fdadb
View on Chainz β†—

Height

#429,071

Difficulty

10.345553

Transactions

1

Size

201 B

Version

2

Bits

0a587628

Nonce

481,908

Timestamp

3/4/2014, 1:01:21 PM

Confirmations

6,371,251

Merkle Root

a0c4f46b0b1ce19975fe1d571e0a82a0990df7465bee04b236ecec5ee4f74dfa
Transactions (1)
Coinbasea0c4f46b0b1ce1…ecec5ee4f74dfa
1 in β†’ 1 out9.3300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

7.101 Γ— 10⁹⁷(98-digit number)
71015686555506549581…62565319988135895040
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
7.101 Γ— 10⁹⁷(98-digit number)
71015686555506549581…62565319988135895039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.101 Γ— 10⁹⁷(98-digit number)
71015686555506549581…62565319988135895041
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
1.420 Γ— 10⁹⁸(99-digit number)
14203137311101309916…25130639976271790079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.420 Γ— 10⁹⁸(99-digit number)
14203137311101309916…25130639976271790081
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
2.840 Γ— 10⁹⁸(99-digit number)
28406274622202619832…50261279952543580159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.840 Γ— 10⁹⁸(99-digit number)
28406274622202619832…50261279952543580161
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
5.681 Γ— 10⁹⁸(99-digit number)
56812549244405239664…00522559905087160319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.681 Γ— 10⁹⁸(99-digit number)
56812549244405239664…00522559905087160321
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
1.136 Γ— 10⁹⁹(100-digit number)
11362509848881047932…01045119810174320639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.136 Γ— 10⁹⁹(100-digit number)
11362509848881047932…01045119810174320641
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 429071

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 76c8046adee448fd9be923f4d3f676e0a75a57999581f20170fe28084a2fdadb

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 #429,071 on Chainz β†—
Circulating Supply:57,646,631 XPMΒ·at block #6,800,321 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