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Home/Chain Registry/Block #2,847,258

Block #2,847,258

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/20/2018, 3:16:48 AM Β· Difficulty 11.7328 Β· 3,992,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72a75002854382608abd6fd575134e8a29b538b7679c0883737a0a69eac28f06
View on Chainz β†—

Difficulty

11.732833

Transactions

1

Size

202 B

Version

2

Bits

0bbb9af0

Nonce

490,233,949

Timestamp

9/20/2018, 3:16:48 AM

Confirmations

3,992,466

Merkle Root

5e0688248791601cc89fac0d3f87d14f9bf036b88841ef982be5ea7286ef3210
Transactions (1)
Coinbase5e068824879160…e5ea7286ef3210
1 in β†’ 1 out7.2500 XPM110 B
AUMQRepm…tAfKmdW1
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.

6.042 Γ— 10⁹⁹(100-digit number)
60426987796443500845…24817977337760972800
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
6.042 Γ— 10⁹⁹(100-digit number)
60426987796443500845…24817977337760972799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.042 Γ— 10⁹⁹(100-digit number)
60426987796443500845…24817977337760972801
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
1.208 Γ— 10¹⁰⁰(101-digit number)
12085397559288700169…49635954675521945599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.208 Γ— 10¹⁰⁰(101-digit number)
12085397559288700169…49635954675521945601
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
2.417 Γ— 10¹⁰⁰(101-digit number)
24170795118577400338…99271909351043891199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.417 Γ— 10¹⁰⁰(101-digit number)
24170795118577400338…99271909351043891201
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
4.834 Γ— 10¹⁰⁰(101-digit number)
48341590237154800676…98543818702087782399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.834 Γ— 10¹⁰⁰(101-digit number)
48341590237154800676…98543818702087782401
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
9.668 Γ— 10¹⁰⁰(101-digit number)
96683180474309601352…97087637404175564799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.668 Γ— 10¹⁰⁰(101-digit number)
96683180474309601352…97087637404175564801
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
1.933 Γ— 10¹⁰¹(102-digit number)
19336636094861920270…94175274808351129599
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 2847258

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 72a75002854382608abd6fd575134e8a29b538b7679c0883737a0a69eac28f06

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 #2,847,258 on Chainz β†—
Circulating Supply:57,962,084 XPMΒ·at block #6,839,723 Β· updates every 60s
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