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Home/Chain Registry/Block #2,691,729

Block #2,691,729

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2018, 4:27:22 PM Β· Difficulty 11.6818 Β· 4,150,141 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffcd7ece43b206de62d58d5792fc309df43aaa66ce1b1038272ab4ea76fde5ae
View on Chainz β†—

Difficulty

11.681815

Transactions

1

Size

200 B

Version

2

Bits

0bae8b72

Nonce

844,411,126

Timestamp

6/4/2018, 4:27:22 PM

Confirmations

4,150,141

Merkle Root

4fa9eb5d7bbbb56d0c712f1c3c594e8e44107290cbde63290f073df1676f6e07
Transactions (1)
Coinbase4fa9eb5d7bbbb5…073df1676f6e07
1 in β†’ 1 out7.3200 XPM109 B
APBa6XSf…ncfVV4HM
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.

1.917 Γ— 10⁹⁷(98-digit number)
19171847374939201256…04258200960033095680
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
1.917 Γ— 10⁹⁷(98-digit number)
19171847374939201256…04258200960033095679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.917 Γ— 10⁹⁷(98-digit number)
19171847374939201256…04258200960033095681
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
3.834 Γ— 10⁹⁷(98-digit number)
38343694749878402513…08516401920066191359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.834 Γ— 10⁹⁷(98-digit number)
38343694749878402513…08516401920066191361
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
7.668 Γ— 10⁹⁷(98-digit number)
76687389499756805027…17032803840132382719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.668 Γ— 10⁹⁷(98-digit number)
76687389499756805027…17032803840132382721
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
1.533 Γ— 10⁹⁸(99-digit number)
15337477899951361005…34065607680264765439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.533 Γ— 10⁹⁸(99-digit number)
15337477899951361005…34065607680264765441
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
3.067 Γ— 10⁹⁸(99-digit number)
30674955799902722011…68131215360529530879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.067 Γ— 10⁹⁸(99-digit number)
30674955799902722011…68131215360529530881
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
6.134 Γ— 10⁹⁸(99-digit number)
61349911599805444022…36262430721059061759
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 2691729

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 ffcd7ece43b206de62d58d5792fc309df43aaa66ce1b1038272ab4ea76fde5ae

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 #2,691,729 on Chainz β†—
Circulating Supply:57,979,337 XPMΒ·at block #6,841,869 Β· updates every 60s
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