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Home/Chain Registry/Block #2,639,913

Block #2,639,913

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 7:54:36 PM Β· Difficulty 11.5584 Β· 4,198,003 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25b695916b41e951cab62c837da5306fee6c51465ffedf1a6999999e8593d13f
View on Chainz β†—

Difficulty

11.558365

Transactions

1

Size

201 B

Version

2

Bits

0b8ef104

Nonce

282,800,120

Timestamp

4/30/2018, 7:54:36 PM

Confirmations

4,198,003

Merkle Root

2206aff181dba9fbec61c54ff7522c734e43be050753afe11e0cd4b1409912a2
Transactions (1)
Coinbase2206aff181dba9…0cd4b1409912a2
1 in β†’ 1 out7.4700 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.040 Γ— 10⁹⁢(97-digit number)
10402792693253129207…00551686496248627200
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
1.040 Γ— 10⁹⁢(97-digit number)
10402792693253129207…00551686496248627199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.040 Γ— 10⁹⁢(97-digit number)
10402792693253129207…00551686496248627201
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
2.080 Γ— 10⁹⁢(97-digit number)
20805585386506258415…01103372992497254399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.080 Γ— 10⁹⁢(97-digit number)
20805585386506258415…01103372992497254401
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
4.161 Γ— 10⁹⁢(97-digit number)
41611170773012516831…02206745984994508799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.161 Γ— 10⁹⁢(97-digit number)
41611170773012516831…02206745984994508801
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
8.322 Γ— 10⁹⁢(97-digit number)
83222341546025033663…04413491969989017599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.322 Γ— 10⁹⁢(97-digit number)
83222341546025033663…04413491969989017601
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
1.664 Γ— 10⁹⁷(98-digit number)
16644468309205006732…08826983939978035199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.664 Γ— 10⁹⁷(98-digit number)
16644468309205006732…08826983939978035201
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
3.328 Γ— 10⁹⁷(98-digit number)
33288936618410013465…17653967879956070399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.328 Γ— 10⁹⁷(98-digit number)
33288936618410013465…17653967879956070401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2639913

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 25b695916b41e951cab62c837da5306fee6c51465ffedf1a6999999e8593d13f

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 #2,639,913 on Chainz β†—
Circulating Supply:57,947,669 XPMΒ·at block #6,837,915 Β· updates every 60s
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