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Block #697,478

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2014, 10:27:28 PM Β· Difficulty 10.9588 Β· 6,103,225 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e992fc13f363e98405dfe0cefb2eafd9da4d2ce8b7a20a4edc1756d367675556
View on Chainz β†—

Height

#697,478

Difficulty

10.958816

Transactions

1

Size

207 B

Version

2

Bits

0af574fd

Nonce

1,543,483,358

Timestamp

8/28/2014, 10:27:28 PM

Confirmations

6,103,225

Merkle Root

fe3e7379138147d991208a345d39ecb4c274a1a7e9de85c45cc87b6c2fc69ba2
Transactions (1)
Coinbasefe3e7379138147…c87b6c2fc69ba2
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.124 Γ— 10⁹⁷(98-digit number)
21240924860219666700…07762833626388561920
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
2.124 Γ— 10⁹⁷(98-digit number)
21240924860219666700…07762833626388561919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.124 Γ— 10⁹⁷(98-digit number)
21240924860219666700…07762833626388561921
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
4.248 Γ— 10⁹⁷(98-digit number)
42481849720439333400…15525667252777123839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.248 Γ— 10⁹⁷(98-digit number)
42481849720439333400…15525667252777123841
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
8.496 Γ— 10⁹⁷(98-digit number)
84963699440878666800…31051334505554247679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.496 Γ— 10⁹⁷(98-digit number)
84963699440878666800…31051334505554247681
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
1.699 Γ— 10⁹⁸(99-digit number)
16992739888175733360…62102669011108495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16992739888175733360…62102669011108495361
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
3.398 Γ— 10⁹⁸(99-digit number)
33985479776351466720…24205338022216990719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.398 Γ— 10⁹⁸(99-digit number)
33985479776351466720…24205338022216990721
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 697478

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 e992fc13f363e98405dfe0cefb2eafd9da4d2ce8b7a20a4edc1756d367675556

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 #697,478 on Chainz β†—
Circulating Supply:57,649,690 XPMΒ·at block #6,800,702 Β· updates every 60s
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