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Block #429,077

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2014, 1:07:08 PM Β· Difficulty 10.3457 Β· 6,385,394 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
865dc2e8f88224b5d969deaa39a3bc23c41b5aa05f6858cf4d2ff72b66409cdb
View on Chainz β†—

Height

#429,077

Difficulty

10.345683

Transactions

2

Size

641 B

Version

2

Bits

0a587eb0

Nonce

55,034

Timestamp

3/4/2014, 1:07:08 PM

Confirmations

6,385,394

Merkle Root

b141cebf3357fa3ac4a7b8ee5d6e1fa8a4ca3a0d06a2b32cd27f26ae2cd362d0
Transactions (2)
Coinbasef37f4392dad453…e5ace09afaba0f
1 in β†’ 1 out9.3400 XPM110 B
AeKNrjNj…1NEq95Ta
1f2fcfca5b5db9…115d7749ecc53b
2 in β†’ 6 out18.6100 XPM441 B
AMjQ7KtU…8YuZUQHgAZH3aBJB…T7FVgZ83AeKNrjNj…1NEq95TaAHCuz9P2…41tUcRdyAKy4P26p…bxEZW13i
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.

8.146 Γ— 10⁹⁴(95-digit number)
81466249000194591019…85070859102114224000
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
8.146 Γ— 10⁹⁴(95-digit number)
81466249000194591019…85070859102114223999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.146 Γ— 10⁹⁴(95-digit number)
81466249000194591019…85070859102114224001
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
1.629 Γ— 10⁹⁡(96-digit number)
16293249800038918203…70141718204228447999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16293249800038918203…70141718204228448001
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
3.258 Γ— 10⁹⁡(96-digit number)
32586499600077836407…40283436408456895999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.258 Γ— 10⁹⁡(96-digit number)
32586499600077836407…40283436408456896001
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
6.517 Γ— 10⁹⁡(96-digit number)
65172999200155672815…80566872816913791999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.517 Γ— 10⁹⁡(96-digit number)
65172999200155672815…80566872816913792001
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
1.303 Γ— 10⁹⁢(97-digit number)
13034599840031134563…61133745633827583999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.303 Γ— 10⁹⁢(97-digit number)
13034599840031134563…61133745633827584001
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 429077

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 865dc2e8f88224b5d969deaa39a3bc23c41b5aa05f6858cf4d2ff72b66409cdb

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 #429,077 on Chainz β†—
Circulating Supply:57,759,842 XPMΒ·at block #6,814,470 Β· updates every 60s
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