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Block #437,767

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/10/2014, 12:39:20 PM Β· Difficulty 10.3600 Β· 6,387,176 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b5fb1d8631dd6cc7a77486e51727d496c343cd4c8a23db2462475f6214fb383
View on Chainz β†—

Height

#437,767

Difficulty

10.359979

Transactions

1

Size

200 B

Version

2

Bits

0a5c278f

Nonce

46,688

Timestamp

3/10/2014, 12:39:20 PM

Confirmations

6,387,176

Merkle Root

10dcdfc387319fe18194af0356845efee34d078374bba141a1cb603109d50a5c
Transactions (1)
Coinbase10dcdfc387319f…cb603109d50a5c
1 in β†’ 1 out9.3000 XPM109 B
AGTqWybB…qRkFCtCF
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.

2.720 Γ— 10⁹⁢(97-digit number)
27204836287563234402…77366829291747425260
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
2.720 Γ— 10⁹⁢(97-digit number)
27204836287563234402…77366829291747425259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.720 Γ— 10⁹⁢(97-digit number)
27204836287563234402…77366829291747425261
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
5.440 Γ— 10⁹⁢(97-digit number)
54409672575126468805…54733658583494850519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.440 Γ— 10⁹⁢(97-digit number)
54409672575126468805…54733658583494850521
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
1.088 Γ— 10⁹⁷(98-digit number)
10881934515025293761…09467317166989701039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10881934515025293761…09467317166989701041
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
2.176 Γ— 10⁹⁷(98-digit number)
21763869030050587522…18934634333979402079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.176 Γ— 10⁹⁷(98-digit number)
21763869030050587522…18934634333979402081
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
4.352 Γ— 10⁹⁷(98-digit number)
43527738060101175044…37869268667958804159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.352 Γ— 10⁹⁷(98-digit number)
43527738060101175044…37869268667958804161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
8.705 Γ— 10⁹⁷(98-digit number)
87055476120202350089…75738537335917608319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 437767

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 4b5fb1d8631dd6cc7a77486e51727d496c343cd4c8a23db2462475f6214fb383

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 #437,767 on Chainz β†—
Circulating Supply:57,843,621 XPMΒ·at block #6,824,942 Β· updates every 60s
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