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Block #2,637,501

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 10:53:09 PM Β· Difficulty 11.4450 Β· 4,195,517 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b9cc2218e58ce199aedb9e8b5e971418ddb799c4cea62d726a961ed6153cc6b
View on Chainz β†—

Difficulty

11.445021

Transactions

1

Size

200 B

Version

2

Bits

0b71ece1

Nonce

201,602,814

Timestamp

4/29/2018, 10:53:09 PM

Confirmations

4,195,517

Merkle Root

516b20cedaf0ba78a72ea2c3a4b3598e12e4886eedd1591ed56ca9fc4599c566
Transactions (1)
Coinbase516b20cedaf0ba…6ca9fc4599c566
1 in β†’ 1 out7.6200 XPM110 B
ARNFeizf…fYoGVA79
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.

4.382 Γ— 10⁹⁴(95-digit number)
43826163183653481137…56132336532880307200
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
4.382 Γ— 10⁹⁴(95-digit number)
43826163183653481137…56132336532880307199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.382 Γ— 10⁹⁴(95-digit number)
43826163183653481137…56132336532880307201
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
8.765 Γ— 10⁹⁴(95-digit number)
87652326367306962275…12264673065760614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.765 Γ— 10⁹⁴(95-digit number)
87652326367306962275…12264673065760614401
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
1.753 Γ— 10⁹⁡(96-digit number)
17530465273461392455…24529346131521228799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.753 Γ— 10⁹⁡(96-digit number)
17530465273461392455…24529346131521228801
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
3.506 Γ— 10⁹⁡(96-digit number)
35060930546922784910…49058692263042457599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.506 Γ— 10⁹⁡(96-digit number)
35060930546922784910…49058692263042457601
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
7.012 Γ— 10⁹⁡(96-digit number)
70121861093845569820…98117384526084915199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.012 Γ— 10⁹⁡(96-digit number)
70121861093845569820…98117384526084915201
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
1.402 Γ— 10⁹⁢(97-digit number)
14024372218769113964…96234769052169830399
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 2637501

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 7b9cc2218e58ce199aedb9e8b5e971418ddb799c4cea62d726a961ed6153cc6b

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 #2,637,501 on Chainz β†—
Circulating Supply:57,908,320 XPMΒ·at block #6,833,017 Β· updates every 60s
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