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Block #898,076

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2015, 1:11:23 AM Β· Difficulty 10.9446 Β· 5,928,808 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e92cbefe7e6e45bfadb6724ebef970d3560419ec90d31b577f7c87db7125a58a
View on Chainz β†—

Height

#898,076

Difficulty

10.944556

Transactions

1

Size

199 B

Version

2

Bits

0af1ce70

Nonce

1,327,859,130

Timestamp

1/17/2015, 1:11:23 AM

Confirmations

5,928,808

Merkle Root

0f826a01c32e2a66f0edb3f2023fa0726ddd0cd2a54248954bfd1e7af5018086
Transactions (1)
Coinbase0f826a01c32e2a…fd1e7af5018086
1 in β†’ 1 out8.3400 XPM109 B
AM3jdvf6…jYW3CWMB
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.

4.189 Γ— 10⁹⁴(95-digit number)
41894729273135887133…01590110523676672000
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
4.189 Γ— 10⁹⁴(95-digit number)
41894729273135887133…01590110523676671999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.189 Γ— 10⁹⁴(95-digit number)
41894729273135887133…01590110523676672001
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
8.378 Γ— 10⁹⁴(95-digit number)
83789458546271774266…03180221047353343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.378 Γ— 10⁹⁴(95-digit number)
83789458546271774266…03180221047353344001
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
1.675 Γ— 10⁹⁡(96-digit number)
16757891709254354853…06360442094706687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.675 Γ— 10⁹⁡(96-digit number)
16757891709254354853…06360442094706688001
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
3.351 Γ— 10⁹⁡(96-digit number)
33515783418508709706…12720884189413375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.351 Γ— 10⁹⁡(96-digit number)
33515783418508709706…12720884189413376001
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
6.703 Γ— 10⁹⁡(96-digit number)
67031566837017419413…25441768378826751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.703 Γ— 10⁹⁡(96-digit number)
67031566837017419413…25441768378826752001
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 898076

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 e92cbefe7e6e45bfadb6724ebef970d3560419ec90d31b577f7c87db7125a58a

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 #898,076 on Chainz β†—
Circulating Supply:57,859,236 XPMΒ·at block #6,826,883 Β· updates every 60s
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