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Home/Chain Registry/Block #2,987,522

Block #2,987,522

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/30/2018, 1:34:16 AM Β· Difficulty 11.2772 Β· 3,856,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4fec8e73f697165a0a42f9650c8a3c7538d3b876ce4217097de7a27f0ee30e97
View on Chainz β†—

Difficulty

11.277241

Transactions

1

Size

202 B

Version

2

Bits

0b46f941

Nonce

1,047,923,483

Timestamp

12/30/2018, 1:34:16 AM

Confirmations

3,856,525

Merkle Root

8a30be490665764fa56045ea4184d8e11d7e3347ca2eba38390a1a5a2722df72
Transactions (1)
Coinbase8a30be49066576…0a1a5a2722df72
1 in β†’ 1 out7.8500 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.229 Γ— 10⁹⁹(100-digit number)
12298205577415925522…44997636553687449600
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
1.229 Γ— 10⁹⁹(100-digit number)
12298205577415925522…44997636553687449599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.229 Γ— 10⁹⁹(100-digit number)
12298205577415925522…44997636553687449601
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
2.459 Γ— 10⁹⁹(100-digit number)
24596411154831851044…89995273107374899199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.459 Γ— 10⁹⁹(100-digit number)
24596411154831851044…89995273107374899201
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
4.919 Γ— 10⁹⁹(100-digit number)
49192822309663702089…79990546214749798399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.919 Γ— 10⁹⁹(100-digit number)
49192822309663702089…79990546214749798401
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
9.838 Γ— 10⁹⁹(100-digit number)
98385644619327404179…59981092429499596799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.838 Γ— 10⁹⁹(100-digit number)
98385644619327404179…59981092429499596801
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
1.967 Γ— 10¹⁰⁰(101-digit number)
19677128923865480835…19962184858999193599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.967 Γ— 10¹⁰⁰(101-digit number)
19677128923865480835…19962184858999193601
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
3.935 Γ— 10¹⁰⁰(101-digit number)
39354257847730961671…39924369717998387199
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 2987522

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 4fec8e73f697165a0a42f9650c8a3c7538d3b876ce4217097de7a27f0ee30e97

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 #2,987,522 on Chainz β†—
Circulating Supply:57,996,746 XPMΒ·at block #6,844,046 Β· updates every 60s
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