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Block #969,604

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/11/2015, 4:56:18 PM Β· Difficulty 10.8321 Β· 5,875,696 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3441241b88d9727efa8dfef92eaba2fa25e8210d471d94caa940cb5e6458d4ec
View on Chainz β†—

Height

#969,604

Difficulty

10.832137

Transactions

1

Size

207 B

Version

2

Bits

0ad506ee

Nonce

107,771,025

Timestamp

3/11/2015, 4:56:18 PM

Confirmations

5,875,696

Merkle Root

69ef134d57d7008d2256d8e845b686ef076d7fa1d08129479e4999be73a8dd2a
Transactions (1)
Coinbase69ef134d57d700…4999be73a8dd2a
1 in β†’ 1 out8.5100 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.

8.449 Γ— 10⁹⁡(96-digit number)
84494878656164712137…03111746308099321080
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
8.449 Γ— 10⁹⁡(96-digit number)
84494878656164712137…03111746308099321079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.449 Γ— 10⁹⁡(96-digit number)
84494878656164712137…03111746308099321081
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
1.689 Γ— 10⁹⁢(97-digit number)
16898975731232942427…06223492616198642159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.689 Γ— 10⁹⁢(97-digit number)
16898975731232942427…06223492616198642161
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
3.379 Γ— 10⁹⁢(97-digit number)
33797951462465884854…12446985232397284319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.379 Γ— 10⁹⁢(97-digit number)
33797951462465884854…12446985232397284321
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
6.759 Γ— 10⁹⁢(97-digit number)
67595902924931769709…24893970464794568639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.759 Γ— 10⁹⁢(97-digit number)
67595902924931769709…24893970464794568641
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
1.351 Γ— 10⁹⁷(98-digit number)
13519180584986353941…49787940929589137279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.351 Γ— 10⁹⁷(98-digit number)
13519180584986353941…49787940929589137281
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 969604

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 3441241b88d9727efa8dfef92eaba2fa25e8210d471d94caa940cb5e6458d4ec

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 #969,604 on Chainz β†—
Circulating Supply:58,006,839 XPMΒ·at block #6,845,299 Β· updates every 60s
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