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Home/Chain Registry/Block #1,387,513

Block #1,387,513

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/27/2015, 2:52:03 PM Β· Difficulty 10.8138 Β· 5,453,579 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c69ea254a10c3820f40d97d2ddb684df059c98beea70d96d2c533ed45f4a44de
View on Chainz β†—

Difficulty

10.813826

Transactions

1

Size

201 B

Version

2

Bits

0ad056e3

Nonce

370,019,183

Timestamp

12/27/2015, 2:52:03 PM

Confirmations

5,453,579

Merkle Root

ccd2d370c179c09162908896f933a62e919352185a9b3c408acdfe7fdf4b785a
Transactions (1)
Coinbaseccd2d370c179c0…cdfe7fdf4b785a
1 in β†’ 1 out8.5400 XPM109 B
AQHX2dga…d1xjmVV9
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.

3.247 Γ— 10⁹⁸(99-digit number)
32478701899915672063…19828283570045583360
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
3.247 Γ— 10⁹⁸(99-digit number)
32478701899915672063…19828283570045583359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.247 Γ— 10⁹⁸(99-digit number)
32478701899915672063…19828283570045583361
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
6.495 Γ— 10⁹⁸(99-digit number)
64957403799831344127…39656567140091166719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.495 Γ— 10⁹⁸(99-digit number)
64957403799831344127…39656567140091166721
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
1.299 Γ— 10⁹⁹(100-digit number)
12991480759966268825…79313134280182333439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.299 Γ— 10⁹⁹(100-digit number)
12991480759966268825…79313134280182333441
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
2.598 Γ— 10⁹⁹(100-digit number)
25982961519932537650…58626268560364666879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.598 Γ— 10⁹⁹(100-digit number)
25982961519932537650…58626268560364666881
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
5.196 Γ— 10⁹⁹(100-digit number)
51965923039865075301…17252537120729333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.196 Γ— 10⁹⁹(100-digit number)
51965923039865075301…17252537120729333761
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 1387513

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 c69ea254a10c3820f40d97d2ddb684df059c98beea70d96d2c533ed45f4a44de

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 #1,387,513 on Chainz β†—
Circulating Supply:57,973,100 XPMΒ·at block #6,841,091 Β· updates every 60s
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