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Home/Chain Registry/Block #1,587,321

Block #1,587,321

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2016, 4:17:09 PM Β· Difficulty 10.6505 Β· 5,249,355 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cc18970420dae981ce7f274869f50e282cc3f145ef9a441d250cde0c0488ea93
View on Chainz β†—

Difficulty

10.650542

Transactions

1

Size

243 B

Version

2

Bits

0aa689e8

Nonce

61,335,586

Timestamp

5/16/2016, 4:17:09 PM

Confirmations

5,249,355

Merkle Root

a2bc1eca5ded39190a62341ae61c508d55044c48aab8a5f4a1781b085c3634c4
Transactions (1)
Coinbasea2bc1eca5ded39…781b085c3634c4
1 in β†’ 2 out8.8000 XPM152 B
AXZf8xqq…hQwCQgXtALPu3s2c…EJXLjVFh
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.

2.457 Γ— 10⁹⁢(97-digit number)
24577952634974759476…35773384889558338560
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
2.457 Γ— 10⁹⁢(97-digit number)
24577952634974759476…35773384889558338559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.457 Γ— 10⁹⁢(97-digit number)
24577952634974759476…35773384889558338561
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
4.915 Γ— 10⁹⁢(97-digit number)
49155905269949518952…71546769779116677119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.915 Γ— 10⁹⁢(97-digit number)
49155905269949518952…71546769779116677121
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
9.831 Γ— 10⁹⁢(97-digit number)
98311810539899037904…43093539558233354239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.831 Γ— 10⁹⁢(97-digit number)
98311810539899037904…43093539558233354241
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
1.966 Γ— 10⁹⁷(98-digit number)
19662362107979807580…86187079116466708479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.966 Γ— 10⁹⁷(98-digit number)
19662362107979807580…86187079116466708481
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
3.932 Γ— 10⁹⁷(98-digit number)
39324724215959615161…72374158232933416959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.932 Γ— 10⁹⁷(98-digit number)
39324724215959615161…72374158232933416961
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 1587321

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 cc18970420dae981ce7f274869f50e282cc3f145ef9a441d250cde0c0488ea93

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 #1,587,321 on Chainz β†—
Circulating Supply:57,937,688 XPMΒ·at block #6,836,675 Β· updates every 60s
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