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Home/Chain Registry/Block #2,639,021

Block #2,639,021

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 12:15:31 PM Β· Difficulty 11.5187 Β· 4,198,098 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4a417f47370cb7b0219e5aa352c6c5b26d1f267e41b8d37d47d02ef74ac4ad0f
View on Chainz β†—

Difficulty

11.518706

Transactions

2

Size

427 B

Version

2

Bits

0b84c9f1

Nonce

179,205,252

Timestamp

4/30/2018, 12:15:31 PM

Confirmations

4,198,098

Merkle Root

5bc6e7cf27980481e0dcfee7e876ea38670e9b3cafa6fe42ef258fcfc980382d
Transactions (2)
Coinbase65c05b9c5fd4e1…51fde72d2d3df6
1 in β†’ 1 out7.5300 XPM110 B
Adqah8zh…1WwoHJ9t
7c8ed22138f2a7…6b198bdc5695c8
1 in β†’ 2 out1.5697 XPM226 B
AGPbRjsz…71WvHNT5AVhXa3fj…Y6pzurwk
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.

9.961 Γ— 10⁹⁢(97-digit number)
99615479067928038093…08645135369524264960
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
9.961 Γ— 10⁹⁢(97-digit number)
99615479067928038093…08645135369524264959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.961 Γ— 10⁹⁢(97-digit number)
99615479067928038093…08645135369524264961
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
1.992 Γ— 10⁹⁷(98-digit number)
19923095813585607618…17290270739048529919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.992 Γ— 10⁹⁷(98-digit number)
19923095813585607618…17290270739048529921
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
3.984 Γ— 10⁹⁷(98-digit number)
39846191627171215237…34580541478097059839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.984 Γ— 10⁹⁷(98-digit number)
39846191627171215237…34580541478097059841
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
7.969 Γ— 10⁹⁷(98-digit number)
79692383254342430474…69161082956194119679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.969 Γ— 10⁹⁷(98-digit number)
79692383254342430474…69161082956194119681
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
1.593 Γ— 10⁹⁸(99-digit number)
15938476650868486094…38322165912388239359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.593 Γ— 10⁹⁸(99-digit number)
15938476650868486094…38322165912388239361
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
3.187 Γ— 10⁹⁸(99-digit number)
31876953301736972189…76644331824776478719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.187 Γ— 10⁹⁸(99-digit number)
31876953301736972189…76644331824776478721
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 2639021

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 4a417f47370cb7b0219e5aa352c6c5b26d1f267e41b8d37d47d02ef74ac4ad0f

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 #2,639,021 on Chainz β†—
Circulating Supply:57,941,261 XPMΒ·at block #6,837,118 Β· updates every 60s
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