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Home/Chain Registry/Block #2,278,045

Block #2,278,045

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2017, 5:38:00 PM Β· Difficulty 10.9553 Β· 4,553,407 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9f0781752bda40874750d784c6abfa9053967ddf0fe01d6d4cb0630769ca9589
View on Chainz β†—

Difficulty

10.955303

Transactions

1

Size

200 B

Version

2

Bits

0af48ec4

Nonce

1,134,816,956

Timestamp

9/1/2017, 5:38:00 PM

Confirmations

4,553,407

Merkle Root

514cc68d11b317ddee3415bd9f48927243e4cc33277ed7c45334864e69c3f10a
Transactions (1)
Coinbase514cc68d11b317…34864e69c3f10a
1 in β†’ 1 out8.3200 XPM109 B
ANszQT4u…VnXVuq8m
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.

3.726 Γ— 10⁹⁷(98-digit number)
37264429011231762707…99389889758017863680
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
3.726 Γ— 10⁹⁷(98-digit number)
37264429011231762707…99389889758017863679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.726 Γ— 10⁹⁷(98-digit number)
37264429011231762707…99389889758017863681
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
7.452 Γ— 10⁹⁷(98-digit number)
74528858022463525414…98779779516035727359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.452 Γ— 10⁹⁷(98-digit number)
74528858022463525414…98779779516035727361
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
1.490 Γ— 10⁹⁸(99-digit number)
14905771604492705082…97559559032071454719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.490 Γ— 10⁹⁸(99-digit number)
14905771604492705082…97559559032071454721
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
2.981 Γ— 10⁹⁸(99-digit number)
29811543208985410165…95119118064142909439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.981 Γ— 10⁹⁸(99-digit number)
29811543208985410165…95119118064142909441
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
5.962 Γ— 10⁹⁸(99-digit number)
59623086417970820331…90238236128285818879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.962 Γ— 10⁹⁸(99-digit number)
59623086417970820331…90238236128285818881
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 2278045

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 9f0781752bda40874750d784c6abfa9053967ddf0fe01d6d4cb0630769ca9589

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 #2,278,045 on Chainz β†—
Circulating Supply:57,895,781 XPMΒ·at block #6,831,451 Β· updates every 60s
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