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Block #901,597

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2015, 5:06:28 PM Β· Difficulty 10.9411 Β· 5,925,083 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e05d9a753a7adbff0417a544afe88b0309a5e146990dcaff1c0c2c33923fc2f
View on Chainz β†—

Height

#901,597

Difficulty

10.941122

Transactions

1

Size

243 B

Version

2

Bits

0af0ed5d

Nonce

733,561,422

Timestamp

1/19/2015, 5:06:28 PM

Confirmations

5,925,083

Merkle Root

4db7c999f3c4d01ffed1e64a0016ff8bdf4bd9b5105b42e82255fece7fe4d416
Transactions (1)
Coinbase4db7c999f3c4d0…55fece7fe4d416
1 in β†’ 2 out8.3400 XPM152 B
AJ2o6sWu…BdumbXQhALPu3s2c…EJXLjVFh
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.

1.425 Γ— 10⁹⁷(98-digit number)
14257522084248209684…97012625423640934400
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
1.425 Γ— 10⁹⁷(98-digit number)
14257522084248209684…97012625423640934399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.425 Γ— 10⁹⁷(98-digit number)
14257522084248209684…97012625423640934401
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
2.851 Γ— 10⁹⁷(98-digit number)
28515044168496419368…94025250847281868799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.851 Γ— 10⁹⁷(98-digit number)
28515044168496419368…94025250847281868801
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
5.703 Γ— 10⁹⁷(98-digit number)
57030088336992838736…88050501694563737599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.703 Γ— 10⁹⁷(98-digit number)
57030088336992838736…88050501694563737601
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
1.140 Γ— 10⁹⁸(99-digit number)
11406017667398567747…76101003389127475199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.140 Γ— 10⁹⁸(99-digit number)
11406017667398567747…76101003389127475201
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
2.281 Γ— 10⁹⁸(99-digit number)
22812035334797135494…52202006778254950399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.281 Γ— 10⁹⁸(99-digit number)
22812035334797135494…52202006778254950401
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 901597

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 4e05d9a753a7adbff0417a544afe88b0309a5e146990dcaff1c0c2c33923fc2f

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 #901,597 on Chainz β†—
Circulating Supply:57,857,589 XPMΒ·at block #6,826,679 Β· updates every 60s
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