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Block #903,307

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/21/2015, 1:19:31 AM Β· Difficulty 10.9385 Β· 5,891,735 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0a4d3bb6c9e81a7924eeae97a012ca2805885de4bd643de5a1a13134b2887c12
View on Chainz β†—

Height

#903,307

Difficulty

10.938543

Transactions

2

Size

3.31 KB

Version

2

Bits

0af0445d

Nonce

1,923,948,088

Timestamp

1/21/2015, 1:19:31 AM

Confirmations

5,891,735

Merkle Root

c815a537d4abaabdcfae40d8c48d09669b9e3705a8f65d2f1d2d1d21d9f58779
Transactions (2)
Coinbased2356aa9ab6ba0…ec89a1f31f0e2f
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
95958fd7e88686…9a933b28090c43
21 in β†’ 2 out3827.0047 XPM3.11 KB
AMkWEzRQ…aT458YyCAZMunvRb…G9pQh9ak
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.

8.900 Γ— 10⁹⁢(97-digit number)
89004436790102388241…47168227684300284800
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
8.900 Γ— 10⁹⁢(97-digit number)
89004436790102388241…47168227684300284799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.900 Γ— 10⁹⁢(97-digit number)
89004436790102388241…47168227684300284801
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
1.780 Γ— 10⁹⁷(98-digit number)
17800887358020477648…94336455368600569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.780 Γ— 10⁹⁷(98-digit number)
17800887358020477648…94336455368600569601
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
3.560 Γ— 10⁹⁷(98-digit number)
35601774716040955296…88672910737201139199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.560 Γ— 10⁹⁷(98-digit number)
35601774716040955296…88672910737201139201
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
7.120 Γ— 10⁹⁷(98-digit number)
71203549432081910593…77345821474402278399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.120 Γ— 10⁹⁷(98-digit number)
71203549432081910593…77345821474402278401
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
1.424 Γ— 10⁹⁸(99-digit number)
14240709886416382118…54691642948804556799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.424 Γ— 10⁹⁸(99-digit number)
14240709886416382118…54691642948804556801
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 903307

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 0a4d3bb6c9e81a7924eeae97a012ca2805885de4bd643de5a1a13134b2887c12

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 #903,307 on Chainz β†—
Circulating Supply:57,604,375 XPMΒ·at block #6,795,041 Β· updates every 60s
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